Monte Carlo Simulation of the Potts Model in 2-5 Dimensions
نویسنده
چکیده
In this paper, I explore the behavior of the Potts model in the parameter space of spin number, lattice size, dimensionality, measuring critical behavior and comparing to the mean field solution. I find that the Potts model exhibits rich behavior for all non-using cases and exhibits a striking symmetry across spin and dimension in terms of mean field applicability. In addition, I present fitted values for the critical exponents β and η at well as critical temperature Tc, and compare to predicted and previously measured values. I conclude discussing the success of my simulations and behavior of the model across the parameter space.
منابع مشابه
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 paramet...
متن کاملFirst Order Phase Transition of the Q-state Potts Model in Two Dimensions
We have calculated the large-q series of the energy cumulants, the magnetization cumulants and the correlation length at the first order phase transition point both in the ordered and disordered phases for the q-state Potts model in two dimensions. The series enables us to estimate the numerical values of the quantities more precisely by a factor of 102−104 than the Monte Carlo simulations. Fro...
متن کاملar X iv : c on d - m at / 9 50 40 70 v 2 1 9 A pr 1 99 5 Si - 95 - 2 The short - time Dynamics of the Critical Potts Model
The universal behaviour of the short-time dynamics of the three state Potts model in two dimensions at criticality is investigated with Monte Carlo methods. The initial increase of the order is observed. The new dynamic exponent θ as well as exponent z and β/ν are determined. The measurements are carried out in the very beginning of the time evolution. The spatial correlation length is found to...
متن کاملThe Critical Behaviour of Potts Models with Symmetry Breaking Fields
The Q-state Potts model in two dimensions in the presence of external magnetic fields is studied. For general Q ≥ 3 special choices of these magnetic fields produce effective models with smaller Z(Q) symmetry (Q < Q). The phase diagram of these models and their critical behaviour are explored by conventional finite-size scaling and conformal invariance. The possibility of multicritical behavior...
متن کاملThree-state chiral Potts models on the triangular lattice: a Monte Carlo study
The q-state chiral Potts model can describe systems that exhibit rich phase diagrams (see, for instance, ref. [l]) and interesting physical properties like commensurate-incommensurate transitions [2]. The chiral Potts model has been extensively studied in the last few years from the point of view of exactly solvable models. Au-Yang et al. discovered integrable cases for the q-state chiral Potts...
متن کامل