### Citations

337 | Practical graph isomorphism
- McKay
- 1981
(Show Context)
Citation Context ...sm test, i.e., the decision whether two given adjacency lists or adjacency matrices describe the same graph modulo relabelling and reordering of edges and nodes. We employed theNAUTY package by McKay =-=[16]-=- which allows very fast isomorphism tests by calculating a canonical representation of the automorphism group of the graphs. By this means, we classified for the first time all star graphs up to order... |

55 | Effects of random defects on the critical behavior of Ising models
- Harris
- 1974
(Show Context)
Citation Context ... phase transitions, depending on the dimension d and the number of states q. Since in the second-order case the specific-heat exponent α is non-negative for this class of models, the Harris criterion =-=[4]-=- suggests for the corresponding disordered systems either the appearance of a new random fixed point (d = 2, q = 3, 4 and d = 3, q = 2) or logarithmic corrections to the pure fixed point (d = 2, q = 2... |

53 |
Asymptotic analysis of power-series expansions.
- Guttmann
- 1989
(Show Context)
Citation Context ...0.25788(1) 1.2714(8) 0.225 0.28382(1) 1.2873(10) 0.3 0.31566(2) 1.305(4) 0.375 0.35557(5) 1.329(4) 0.45 0.40743(10) 1.365(6) 0.525 0.4772(2) 1.400(10) 0.6 0.576(1) 1.435(60) differential approximants =-=[28,29]-=-, the Baker-Hunter method [30] or the methods M1 and M2 [31], especially tailored to deal with confluent singularities as one would expect in a crossover situation, give improved results in the pure (... |

24 |
Logarithmic Correlations in Quenched Random Magnets and Polymers.
- Cardy
(Show Context)
Citation Context ...ation techniques in disordered systems, where the singularity structure of the free energy or susceptibility may be very complicated, involving Griffiths-type singularities or logarithmic corrections =-=[3]-=-. Pure Potts models show either first- or second-order phase transitions, depending on the dimension d and the number of states q. Since in the second-order case the specific-heat exponent α is non-ne... |

24 |
Rounding of first-order phase transitions in systems with quenched disorder,”
- Aizenman, Wehr
- 1989
(Show Context)
Citation Context ...mic corrections to the pure fixed point (d = 2, q = 2). At first-order phase transitions, randomness softens the transitions [5]. For d = 2 even infinitesimal disorder induces a continuous transition =-=[6,7]-=-, whereas for d = 3, q > 2 a tricritical point at a finite disorder strength is expected [8]. In this work we studied these scenarios by means of “star-graph” high-temperature series expansions where ... |

22 |
Precise determination of the bond percolation thresholds and finite-size scaling corrections for the sc, fcc, and bcc lattices,
- Lorenz, Ziff
- 1998
(Show Context)
Citation Context ... ratios for different values of p. For small p they show the typical oscillations related to the existence of an antiferromagnetic singularity at −vc. Near the percolation threshold at pc = 0.751 188 =-=[25]-=- (where Tc goes to 0, vc to 1) the series is clearly ill-behaved, related to the exp(1/T) singularity expected there. Besides that, the slope (related to γ) is increasing with p. The widely used DLog-... |

9 |
Random-field mechanism in random-bond multicritical systems,”
- Hui, Berker
- 1989
(Show Context)
Citation Context ...mic corrections to the pure fixed point (d = 2, q = 2). At first-order phase transitions, randomness softens the transitions [5]. For d = 2 even infinitesimal disorder induces a continuous transition =-=[6,7]-=-, whereas for d = 3, q > 2 a tricritical point at a finite disorder strength is expected [8]. In this work we studied these scenarios by means of “star-graph” high-temperature series expansions where ... |

9 |
Computer Techniques for Evaluating Lattice Constants, Phase Transitions and Critical Phenomena ,Eds
- Martin
- 1974
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Citation Context ...G) − ∑ g⊂G WF(g), resulting for an infinite (e.g. hypercubic) lattice in F(Z d ) = ∑ G (G : Zd ) WF(G), where (G : Zd ) denotes the weak embedding number of the graph G in the given lattice structure =-=[15]-=-. The following observation makes this a useful method: Let G be a graph with an articulation vertex where two star subgraphs G1,2 are glued together. Then WF(G) vanishes if F(G) = F(G1) + F(G2). An o... |

8 |
Influence of quenched impurities on first-order phase transitions
- Imry, Wortis
- 1979
(Show Context)
Citation Context ... of a new random fixed point (d = 2, q = 3, 4 and d = 3, q = 2) or logarithmic corrections to the pure fixed point (d = 2, q = 2). At first-order phase transitions, randomness softens the transitions =-=[5]-=-. For d = 2 even infinitesimal disorder induces a continuous transition [6,7], whereas for d = 3, q > 2 a tricritical point at a finite disorder strength is expected [8]. In this work we studied these... |

8 | Randomly dilute spin models: A six-loop field-theoretic study.
- Pelissetto, Vicari
- 2000
(Show Context)
Citation Context ...ven in Table 2 are at least compatible with Monte Carlo results for site and bond dilution [26,32,33] which cluster quite sharply around γMC = 1.34(1). Field-theoretic renormalization group estimates =-=[21,34]-=- favor slightly smaller exponents of γRG = 1.32 – 1.33, while experiments [18–20] report values between γexp = 1.31 – 1.44, cp., e.g., the table in Ref. [35]. 4.2. Bond-diluted 4-state Potts model In ... |

7 |
Star-graph expansions for bond-diluted Potts models, Phys
- Hellmund, Janke
(Show Context)
Citation Context ...to a second-order transition governed by a disorder fixed point. In the latter regime we are interested in locating power-law divergences of the form (8) from our susceptibility series up to order 18 =-=[37,38]-=-. To localize a first-order transition point, however, a high-temperature series alone is not sufficient since there the correlation length remains finite and no critical singularity occurs. In analys... |

6 |
eds., Series Expansions for Lattice Models
- Domb, Green
- 1974
(Show Context)
Citation Context ...Ising, Potts, etc.), 64.60.Fr Equilibrium properties near critical points, critical exponents, 75.10.Hk Classical spin models, 75.10.Nr Spin-glass and other random models Systematic series expansions =-=[1]-=- for statistical physics models defined on a lattice provide an useful complement to field-theoretical renormalization group studies and large-scale numerical Monte Carlo simulations. This is in parti... |

6 |
Series expansions for the Ising spin glass in general dimension, Phys
- Klein, Adler, et al.
- 1991
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Citation Context ... 1.305(4) 0.375 0.35557(5) 1.329(4) 0.45 0.40743(10) 1.365(6) 0.525 0.4772(2) 1.400(10) 0.6 0.576(1) 1.435(60) differential approximants [28,29], the Baker-Hunter method [30] or the methods M1 and M2 =-=[31]-=-, especially tailored to deal with confluent singularities as one would expect in a crossover situation, give improved results in the pure (p = 0) case but do not essentially change the results in the... |

6 | Critical exponents of the three-dimensional diluted Ising model, Phys
- Ballesteros, Fernández, et al.
- 1998
(Show Context)
Citation Context ... shown. 9Hellmund and Janke central disorder regime, p = 0.3 – 0.5, the high-temperature series estimates given in Table 2 are at least compatible with Monte Carlo results for site and bond dilution =-=[26,32,33]-=- which cluster quite sharply around γMC = 1.34(1). Field-theoretic renormalization group estimates [21,34] favor slightly smaller exponents of γRG = 1.32 – 1.33, while experiments [18–20] report value... |

5 |
High-temperature series expansion for spin glasses
- Singh, Chakravarty
- 1987
(Show Context)
Citation Context ...e star-graph technique. Nonetheless, the linked-cluster method has not yet been applied to problems with quenched disorder. The star-graph method can be adopted to systems involving quenched disorder =-=[12,13]-=- (as also can the no-free-end method [14]) since it allows one to take the disorder average on the level of individual graphs. The basic idea is to assemble the value of some extensive thermodynamic q... |

5 |
Renormalized (1/σ) expansion for lattice animals and localization
- Harris
- 1982
(Show Context)
Citation Context ...ked-cluster method has not yet been applied to problems with quenched disorder. The star-graph method can be adopted to systems involving quenched disorder [12,13] (as also can the no-free-end method =-=[14]-=-) since it allows one to take the disorder average on the level of individual graphs. The basic idea is to assemble the value of some extensive thermodynamic quantity F on a large or even infinite gra... |

5 |
Effective and asymptotic critical exponents of weakly diluted quenched Ising model: 3d approach versus √ ǫ-expansion, Phys
- Folk, Holovatch, et al.
- 2000
(Show Context)
Citation Context ... Ising model universality class have been studied extensively in experiments [18–20] and also by field theoretical and numerical methods. A comprehensive compilation of recent results can be found in =-=[21]-=-, showing a wide scatter in the critical exponents of different groups, presumably due to large crossover effects. Our high-temperature series expansion for the susceptibility up to order 19 is given ... |

5 |
High-temperature series expansions for random-bond Potts models
- Hellmund, Janke
- 2002
(Show Context)
Citation Context ...erent groups, presumably due to large crossover effects. Our high-temperature series expansion for the susceptibility up to order 19 is given with coefficients as polynomials in p, χ(v) = ∑ n an(p)vn =-=[22]-=-. Therefore it should be well-suited for the method of partial differential approximants [23] which was successfully used to analyse series with an anisotropy parameter describing the crossover betwee... |

5 |
Bicriticality and partial differential approximants, in Phase Transitions: Cargèse 1980, edited by M
- Fisher, Chen
- 1982
(Show Context)
Citation Context ...n for the susceptibility up to order 19 is given with coefficients as polynomials in p, χ(v) = ∑ n an(p)vn [22]. Therefore it should be well-suited for the method of partial differential approximants =-=[23]-=- which was successfully used to analyse series with an anisotropy parameter describing the crossover between 3D Ising, XY and Heisenberg behaviour [24]. But this method was unable to give conclusive r... |

5 |
Two-dimensional Ising-like systems: Corrections to scaling in the Klauder and double-Gaussian models
- Barma, Fisher
- 1985
(Show Context)
Citation Context ...ollowing sharp increase is to be interpreted as due to the crossover to the percolation fixed point at pc ≈ 0.75, Tc = 0, where a χ ∼ exp(1/T) behaviour is expected. It is well known (see, e.g., Ref. =-=[40]-=-) that series analysis in crossover situations is extremely difficult. If the parameter p interpolates between regions governed by different fixed points, the exponent obtained from a finite number of... |

4 |
Critical behaviour of random-bond Potts models
- Cardy, Jacobsen
- 1997
(Show Context)
Citation Context ...omness softens the transitions [5]. For d = 2 even infinitesimal disorder induces a continuous transition [6,7], whereas for d = 3, q > 2 a tricritical point at a finite disorder strength is expected =-=[8]-=-. In this work we studied these scenarios by means of “star-graph” high-temperature series expansions where the disorder average can be taken at the level of individual graphs. Using optimized cluster... |

4 |
The Ising ferromagnet with impurities: A series expansion approach
- Rapaport
- 1972
(Show Context)
Citation Context ...e star-graph technique. Nonetheless, the linked-cluster method has not yet been applied to problems with quenched disorder. The star-graph method can be adopted to systems involving quenched disorder =-=[12,13]-=- (as also can the no-free-end method [14]) since it allows one to take the disorder average on the level of individual graphs. The basic idea is to assemble the value of some extensive thermodynamic q... |

4 | Crossover from random-exchange to random-field critical behavior in FexZn1−xF2, Phys - Belanger, King, et al. - 1986 |

4 |
Yang Inhomogeneous differential approximants for power series
- Fisher, Au
- 1979
(Show Context)
Citation Context ...0.25788(1) 1.2714(8) 0.225 0.28382(1) 1.2873(10) 0.3 0.31566(2) 1.305(4) 0.375 0.35557(5) 1.329(4) 0.45 0.40743(10) 1.365(6) 0.525 0.4772(2) 1.400(10) 0.6 0.576(1) 1.435(60) differential approximants =-=[28,29]-=-, the Baker-Hunter method [30] or the methods M1 and M2 [31], especially tailored to deal with confluent singularities as one would expect in a crossover situation, give improved results in the pure (... |

4 |
Jr., “Methods of series analysis
- Baker
- 1979
(Show Context)
Citation Context ...2(1) 1.2873(10) 0.3 0.31566(2) 1.305(4) 0.375 0.35557(5) 1.329(4) 0.45 0.40743(10) 1.365(6) 0.525 0.4772(2) 1.400(10) 0.6 0.576(1) 1.435(60) differential approximants [28,29], the Baker-Hunter method =-=[30]-=- or the methods M1 and M2 [31], especially tailored to deal with confluent singularities as one would expect in a crossover situation, give improved results in the pure (p = 0) case but do not essenti... |

4 |
Three-dimensional randomly dilute Ising model: Monte Carlo results
- Calabrese, Martín-Mayor, et al.
- 2003
(Show Context)
Citation Context ... shown. 9Hellmund and Janke central disorder regime, p = 0.3 – 0.5, the high-temperature series estimates given in Table 2 are at least compatible with Monte Carlo results for site and bond dilution =-=[26,32,33]-=- which cluster quite sharply around γMC = 1.34(1). Field-theoretic renormalization group estimates [21,34] favor slightly smaller exponents of γRG = 1.32 – 1.33, while experiments [18–20] report value... |

4 |
Random Ising model in three dimensions: theory, experiment and simulation – a difficult coexistence, preprint cond-mat/0411255
- Berche, Berche, et al.
(Show Context)
Citation Context ...eoretic renormalization group estimates [21,34] favor slightly smaller exponents of γRG = 1.32 – 1.33, while experiments [18–20] report values between γexp = 1.31 – 1.44, cp., e.g., the table in Ref. =-=[35]-=-. 4.2. Bond-diluted 4-state Potts model In three dimensions the 4-state Potts model exhibits in the pure case a strong first-order transition [36] which is expected to stay first order up to some fini... |

4 |
Random-bond Potts models on hypercubic lattices: Hightemperature series expansions
- Hellmund, Janke
- 2002
(Show Context)
Citation Context ...to a second-order transition governed by a disorder fixed point. In the latter regime we are interested in locating power-law divergences of the form (8) from our susceptibility series up to order 18 =-=[37,38]-=-. To localize a first-order transition point, however, a high-temperature series alone is not sufficient since there the correlation length remains finite and no critical singularity occurs. In analys... |

4 |
Softening of first-order transition in three-dimensions by quenched disorder.
- Chatelain, Berche, et al.
- 2001
(Show Context)
Citation Context ... c 0.6 -0.01 0 0.2 0.4 0.6 0 0.1 0.2 0.3 0.4 0.5 0.6 p Figure 6. Transition temperatures of the bond-diluted 4-state Potts model for different dilution p as obtained from Monte Carlo (MC) simulations =-=[39]-=- and DLog-Padé series analyses. The inset shows the difference between the two estimates. 30 Padé approximants for each value of p, 2 with the results of recent Monte Carlo simulations [39]. For small... |

3 |
Weak quenched disorder and criticality: Resummation of asymptotic(?) series
- Holovatch, Blavats’ka, et al.
- 2002
(Show Context)
Citation Context ... and large-scale numerical Monte Carlo simulations. This is in particular true when studying phase transitions and critical phenomena of quenched, disordered systems. In the field-theoretic treatment =-=[2]-=- the necessary average over disorder realizations at the level of the free energy requires the application of the so-called “replica trick” which loosely speaking introduces n different, interacting c... |

3 |
Higher orders of the high-temperature expansion for the Ising model in three dimensions
- Arisue, Fujiwara, et al.
- 2004
(Show Context)
Citation Context ...und and Janke [9] exploits ideas from so-called finite-lattice methods, usually employed before for the generation of low-temperature series. Using a clever reformulation of the method, Arisue et al. =-=[10]-=- succeeded to generate a very impressive 32th order world-record high-temperature susceptibility series for the pure Ising model in three dimensions. For the class of classical O(N) spin models withou... |

3 |
A library of extended high-temperature expansions of basic observables for the spin S Ising models on two- and three-dimensional lattices
- Butera, Comi
- 2002
(Show Context)
Citation Context ...s for the pure Ising model in three dimensions. For the class of classical O(N) spin models without disorder, quite long series (up to order β25 ) have also been produced by linked-cluster expansions =-=[11]-=-. This technique also allows one to obtain series for more involved observables (such as the second moment of the spin-spin correlation function yielding the correlation length) which have no star-gra... |

3 | Critical behavior of the three-dimensional site-random Ising magnet - Mitchell, Cowley, et al. - 1986 |

3 |
Series analysis of tricritical behaviour: Mean-field model and partial differential approximants
- Salman, Adler
- 1979
(Show Context)
Citation Context ... the method of partial differential approximants [23] which was successfully used to analyse series with an anisotropy parameter describing the crossover between 3D Ising, XY and Heisenberg behaviour =-=[24]-=-. But this method was unable to give conclusive results. Therefore we confined ourselves to a singleparameter series for selected values of p. The ratio method assumes that the expected singularity of... |

3 |
dilution in the 3D Ising model: A Monte Carlo study, Eur
- Berche, Chatelain, et al.
- 2004
(Show Context)
Citation Context ...g again inconclusive near the percolation threshold. Nevertheless, up to about p = 0.6 the series estimates for vc respectively Tc are in perfect agreement 1 with the Monte Carlo (MC) results of Ref. =-=[26]-=-. This is demonstrated in Fig. 4 where also the (properly normalized) mean-field and effective-medium approximation [27] are shown for comparison. The critical exponent γ, as provided by this method, ... |

3 |
Effective-medium approximation for quenched bond-disorder in the Ising model, Phys
- Turban
- 1980
(Show Context)
Citation Context ...ctively Tc are in perfect agreement 1 with the Monte Carlo (MC) results of Ref. [26]. This is demonstrated in Fig. 4 where also the (properly normalized) mean-field and effective-medium approximation =-=[27]-=- are shown for comparison. The critical exponent γ, as provided by this method, apparently varies with the disorder strength. More sophisticated analysis methods, such as inhomogeneous 1 Notice that “... |

2 |
Algorithm of the finite-lattice method for high-temperature expansion of the Ising model in three dimensions, Phys
- Arisue, Fujiwara
- 2003
(Show Context)
Citation Context ...e systematic generation of high-temperature series expansions which differ in the way relevant subgraphs are selected or grouped together. A recently developed alternative method 3Hellmund and Janke =-=[9]-=- exploits ideas from so-called finite-lattice methods, usually employed before for the generation of low-temperature series. Using a clever reformulation of the method, Arisue et al. [10] succeeded to... |

2 | Critical behavior of a site-diluted three-dimensional Ising magnet, Phys - Birgeneau, Cowley, et al. - 1983 |

2 |
Simulation of 3D q-state Potts models with the multibondic algorithm, unpublished
- Janke, Kappler
(Show Context)
Citation Context ...ween γexp = 1.31 – 1.44, cp., e.g., the table in Ref. [35]. 4.2. Bond-diluted 4-state Potts model In three dimensions the 4-state Potts model exhibits in the pure case a strong first-order transition =-=[36]-=- which is expected to stay first order up to some finite disorder strength, before it gets softened to a second-order transition governed by a disorder fixed point. In the latter regime we are interes... |