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

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.