Critical Behavior of Ferromagnetic Ising Model on Triangular Lattice

TL;DR

This study investigates the critical behavior of the 2D ferromagnetic Ising model on a triangular lattice using a novel updating algorithm, providing highly accurate critical exponents and confirming the continuous nature of the phase transition.

Contribution

The paper introduces a new spin updating algorithm that improves the accuracy of critical exponent estimates for the Ising model on a triangular lattice.

Findings

Transition is continuous at Tc=3.6403(2).

Critical exponents closely match theoretical predictions.

The new algorithm outperforms traditional Monte Carlo methods.

Abstract

We apply a new updating algorithm scheme to investigate the critical behavior of the two-dimensional ferromagnetic Ising model on a triangular lattice with nearest neighbour interactions. The transition is examined by generating accurate data for large lattices with $L=8,10,12,15,20,25,30,40,50$. The spin updating algorithm we employ has the advantages of both metropolis and single-update methods. Our study indicates that the transition to be continuous at $T_c=3.6403(2)$. A convincing finite-size scaling analysis of the model yield $\nu=0.9995(21)$, $\beta/\nu=0.12400(18)$, $\gamma/\nu=1.75223(22)$, $\gamma'/\nu=1.7555(22)$, $\alpha/\nu=0.00077(420)$ (scaling) and $\alpha/\nu=0.0010(42)$(hyperscaling) respectively. Estimates of present scheme yield accurate estimates for all critical exponents than those obtained with Monte Carlo methods and show an excellent agreement with their well-established predicted values.