On Critical Temperature and Finite Size Scaling of Continuous Spin $2d$ Ising Model

TL;DR

This study uses Monte Carlo simulations to analyze the critical temperature and finite size scaling of a continuous spin 2D Ising model, confirming its second order phase transition and universality class.

Contribution

It provides the first detailed finite size scaling analysis of a continuous spin 2D Ising model, including critical temperature and exponents, aligning with the standard 2D Ising universality class.

Findings

Critical temperature approximately 0.925

Second order phase transition observed

Critical exponents match 2D Ising universality class

Abstract

In this paper, we have studied the critical temperature $T_c$ of continuous spin $2d$ square-lattice Ising model using Monte-Carlo simulation. We have considered spins $s$ in a bounded interval, where $s \in [-1,+1]$ in square-lattice configuration with periodic boundary condition. We have observed that the critical temperature $T_c$ is approximately $0.925$, showing a clear second order phase transition. Considering finite size scaling, we have also obtained the critical exponents associated with susceptibility, specific heat, magnetization and we find that these values are in good agreement with the corresponding values obtained for the standard $2d$ Ising universality class.