Logarithmic Corrections and Finite-Size Scaling in the Two-Dimensional 4-State Potts Model

We analyze the scaling and finite-size-scaling behavior of the two-dimensional 4-state Potts model. We find new multiplicative logarithmic corrections for the susceptibility, in addition to the already known ones for the specific heat. We also find additive logarithmic corrections to scaling, some of which are universal. We have checked the theoretical predictions at criticality and off criticality by means of high-precision Monte Carlo data.

[1]  Observation of FSS for a first-order phase transition , 1992, hep-lat/9211014.

[2]  A. Sokal,et al.  Regularity properties and pathologies of position-space renormalization-group transformations: Scope and limitations of Gibbsian theory , 1991, hep-lat/9210032.

[3]  Cluster method for the Ashkin-Teller model. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[4]  Alan D. Sokal,et al.  Dynamic critical behavior of the Swendsen-Wang algorithm: The two-dimensional three-state Potts model revisited , 1997 .

[5]  V. J. Emery,et al.  Critical properties of two-dimensional models , 1981 .

[6]  M. Schick,et al.  First and Second Order Phase Transitions in Potts Models: Renormalization - Group Solution , 1979 .

[7]  Bernard Nienhuis,et al.  Critical behavior of two-dimensional spin models and charge asymmetry in the Coulomb gas , 1984 .

[8]  J. Gunton,et al.  Renormalization group in critical phenomena and quantum field theory : proceedings of a conference,Temple University, May 29-31, 1973 , 1973 .

[9]  L. Schulman In: Finite size scaling and numerical simulation of statistical systems , 1990 .

[10]  M. den Nijs,et al.  A relation between the temperature exponents of the eight-vertex and q-state Potts model , 1979 .

[11]  Borgs,et al.  Finite-size effects at asymmetric first-order phase transitions. , 1992, Physical review letters.

[12]  R. Baxter Exactly solved models in statistical mechanics , 1982 .

[13]  Li,et al.  Rigorous lower bound on the dynamic critical exponents of the Swendsen-Wang algorithm. , 1989, Physical review letters.

[14]  C. Borgs,et al.  A rigorous theory of finite-size scaling at first-order phase transitions , 1990 .

[15]  Kim Application of finite size scaling to Monte Carlo simulations. , 1993, Physical review letters.

[16]  Ferreira,et al.  Extrapolating Monte Carlo simulations to infinite volume: Finite-size scaling at xi /L >> 1. , 1995, Physical review letters.

[17]  C. Hamer,et al.  Logarithmic corrections to finite-size scaling in the four-state Potts model , 1988 .

[18]  R. Baxter,et al.  Exact Solution of an Ising Model with Three-Spin Interactions on a Triangular Lattice , 1973 .

[19]  A. Sokal,et al.  The pivot algorithm: A highly efficient Monte Carlo method for the self-avoiding walk , 1988 .

[20]  R. Pearson Conjecture for the extended Potts model magnetic eigenvalue , 1980 .

[21]  D. Scalapino,et al.  Singularities and Scaling Functions at the Potts-Model Multicritical Point , 1980 .

[22]  M. Nijs Extended scaling relations for the magnetic critical exponents of the Potts model , 1983 .

[23]  B. Nienhuis,et al.  Analytical calculation of two leading exponents of the dilute Potts model , 1982 .

[24]  J. Cardy,et al.  Scaling Theory of the Potts Model Multicritical Point , 1980 .

[25]  C. Borgs,et al.  Finite-size scaling for Potts models , 1991 .

[26]  Wang,et al.  Nonuniversal critical dynamics in Monte Carlo simulations. , 1987, Physical review letters.

[27]  R. Swendsen,et al.  Monte Carlo renormalization-group studies of q-state Potts models in two dimensions , 1980 .

[28]  H. D. Watson At 14 , 1979 .

[29]  É. Brézin,et al.  Critical behavior of uniaxial systems with strong dipolar interactions , 1976 .

[30]  John K. Tomfohr,et al.  Lecture Notes on Physics , 1879, Nature.