Critical behaviour of the Ising S=1/2 and S=1 model on (3,4,6,4) and (3,3,3,3,6) Archimedean lattices

TL;DR

This study uses Monte Carlo simulations to analyze the critical behavior of S=1/2 and S=1 Ising models on specific Archimedean lattices, revealing differences in critical temperatures and exponents compared to the S=1/2 case and other lattices.

Contribution

It provides new critical temperature and exponent data for S=1 Ising models on (3,4,6,4) and (3,3,3,3,6) lattices, expanding understanding of spin models on complex lattices.

Findings

Critical temperatures for S=1 are 1.590(3) and 2.100(4).

Critical exponents differ from S=1/2 models and square lattice.

Effective dimensionality is approximately 1.82 and 1.64 for the two lattices.

Abstract

We investigate the critical properties of the Ising S=1/2 and S=1 model on (3,4,6,4) and (3,3,3,3,6) Archimedean lattices. The system is studied through the extensive Monte Carlo simulations. We calculate the critical temperature as well as the critical point exponents gamma/nu, beta/nu and nu basing on finite size scaling analysis. The calculated values of the critical temperature for S=1 are k_BT_C/J=1.590(3) and k_BT_C/J=2.100(4) for (3,4,6,4) and (3,3,3,3,6) Archimedean lattices, respectively. The critical exponents beta/nu, gamma/nu and 1/nu for S=1 are beta/nu=0.180(20), gamma/nu=1.46(8) and 1/nu=0.83(5) for (3,4,6,4) and 0.103(8), 1.44(8) and 0.94(5) for (3,3,3,3,6) Archimedean lattices. Obtained results differ from the Ising S=1/2 model on (3,4,6,4), (3,3,3,3,6) and square lattice. The evaluated effective dimensionality of the system for S=1 are D_{eff}=1.82(4) for (3,4,6,4) and D_{eff}=1.64(5) for (3,3,3,3,6).