High-Temperature Series Expansions for Random Potts Models

We discuss recently generated high-temperature series expansions for the free energy and the susceptibility of random-bond q-state Potts models on hypercubic lattices. Using the star-graph expansion technique quenched disorder averages can be calculated exactly for arbitrary uncorrelated coupling distributions while keeping the disorder strength p as well as the dimension d as symbolic parameters. We present analyses of the new series for the susceptibility of the Ising (q=2) and 4-state Potts model in three dimensions up to order 19 and 18, respectively, and compare our findings with results from field-theoretical renormalization group studies and Monte Carlo simulations.

[1]  W. Janke,et al.  Random Ising model in three dimensions: theory, experiment and simulation - a difficult coexistence , 2004, Condensed Matter Physics.

[2]  Wolfhard Janke,et al.  Bond dilution in the 3D Ising model: a Monte Carlo study , 2004, cond-mat/0402596.

[3]  W. Janke,et al.  Bond dilution in the 3 D Ising model : a Monte Carlo study , 2004 .

[4]  T. Fujiwara,et al.  Higher orders of the high-temperature expansion for the Ising model in three dimensions , 2003, hep-lat/0309158.

[5]  A. Pelissetto,et al.  Three-dimensional randomly dilute Ising model: Monte Carlo results. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[6]  T. Fujiwara,et al.  Algorithm of the finite-lattice method for high-temperature expansion of the Ising model in three dimensions. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[7]  M. Hellmund,et al.  Star-graph expansions for bond-diluted Potts models. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[8]  M. Hellmund,et al.  High-temperature series expansions for random-bond Potts models on Zd , 2002 .

[9]  P. Butera,et al.  An On-Line Library of Extended High-Temperature Expansions of Basic Observables for the Spin-S Ising Models on Two- and Three-Dimensional Lattices , 2002, hep-lat/0204007.

[10]  M. Hellmund,et al.  Random-bond Potts models on hypercubic lattices: high-temperature series expansions* , 2002 .

[11]  William H. Press,et al.  Numerical recipes in C , 2002 .

[12]  C. V. Ferber,et al.  Weak quenched disorder and criticality: resummation of asymptotic(?) series , 2001, cond-mat/0111158.

[13]  W. Janke,et al.  Softening of first-order transition in three-dimensions by quenched disorder. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[14]  A. Pelissetto,et al.  Randomly dilute spin models: A six-loop field-theoretic study , 2000, cond-mat/0002402.

[15]  J. Cardy Logarithmic Correlations in Quenched Random Magnets and Polymers , 1999, cond-mat/9911024.

[16]  R. Folk,et al.  Effective and Asymptotic Critical Exponents of Weakly Diluted Quenched Ising Model: 3d Approach Versus $ε^{1/2}$-Expansion , 1999, cond-mat/9909121.

[17]  Wolfhard Janke,et al.  Dynamical Behavior of the Multibondic and Multicanonic Algorithm In The 3D q-State Potts Model , 1998 .

[18]  G. Parisi,et al.  Critical exponents of the three dimensional diluted Ising model , 1998, cond-mat/9802273.

[19]  U. Michigan,et al.  Precise determination of the bond percolation thresholds and finite-size scaling corrections for the sc, fcc, and bcc lattices , 1997, cond-mat/9710044.

[20]  J. Cardy,et al.  CRITICAL BEHAVIOR OF RANDOM-BOND POTTS MODELS , 1997, cond-mat/9705038.

[21]  J. Adler,et al.  Series analysis of tricritical behaviour: mean-field model and partial differential approximants , 1997 .

[22]  Klein,et al.  Series expansions for the Ising spin glass in general dimension. , 1991, Physical review. B, Condensed matter.

[23]  Berker,et al.  Random-field mechanism in random-bond multicritical systems. , 1989, Physical review letters.

[24]  J. Wehr,et al.  Rounding of first-order phase transitions in systems with quenched disorder. , 1989, Physical review letters.

[25]  Chakravarty,et al.  High-temperature series expansion for spin glasses. I. Derivation of the series. , 1987, Physical Review B (Condensed Matter).

[26]  Yoshizawa,et al.  Critical behavior of the three-dimensional site-random Ising magnet: MnxZn1-xF2. , 1986, Physical review. B, Condensed matter.

[27]  King,et al.  Crossover from random-exchange to random-field critical behavior in FexZn1-xF2. , 1986, Physical Review B (Condensed Matter).

[28]  Fisher,et al.  Two-dimensional Ising-like systems: Corrections to scaling in the Klauder and double-Gaussian models. , 1985, Physical review. B, Condensed matter.

[29]  R. Birgeneau,et al.  Critical behavior of a site-diluted three-dimensional Ising magnet , 1983 .

[30]  A. B. Harris,et al.  Renormalized (1σ) expansion for lattice animals and localization , 1982 .

[31]  M. Fisher,et al.  Bicriticality and Partial Differential Approximants , 1982 .

[32]  M. Fisher,et al.  Inhomogeneous differential approximants for power series , 1980 .

[33]  L. Turban Effective-medium approximation for quenched bond-disorder in the Ising model , 1980 .

[34]  Y. Imry,et al.  Influence of quenched impurities on first-order phase transitions , 1979 .

[35]  A. B. Harris,et al.  Effect of random defects on the critical behaviour of Ising models , 1974 .

[36]  C. Domb,et al.  Series expansions for lattice models , 1974 .

[37]  G. A. Baker,et al.  Methods of Series Analysis. II. Generalized and Extended Methods with Application to the Ising Model , 1973 .

[38]  D. Rapaport The Ising ferromagnet with impurities : a series expansion approach: I , 1972 .