Exploring Different Extrapolation Approaches for the Critical Temperature of the 2D-Ising Model Based on Exactly...

Area of Science:

• Statistical mechanics
• Condensed matter physics
• Computational physics

Background:

• The 2D Ising model is a fundamental benchmark in statistical mechanics, exhibiting a critical phase transition.
• Accurate determination of the critical temperature (Tc) is essential for understanding its behavior.
• Previous work introduced an approximate free-energy expression for finite 2D Ising lattices.

Purpose of the Study:

• To investigate and compare different extrapolation strategies for estimating the infinite system's critical temperature (Tc) from finite 2D Ising lattices.
• To evaluate the effectiveness of scaling models and envelope constructions for Tc estimation.
• To compare these novel methods with the established Binder cumulant method.

Main Methods:

• Analysis of finite square lattices (N x N) with free and periodic boundary conditions.
• Computation of heat capacity profiles C(T) by exploiting the exactly accessible density of states.
• Application of scaling models for the peak temperature Tmax(N) and an envelope construction method.
• Comparison with the Binder cumulant method for validation.

Main Results:

• Both scaling models for Tmax(N) and the envelope construction method converge to the same asymptotic value for Tc.
• These novel extrapolation strategies compare favorably to the Binder cumulant method.
• A simple N/(N+1)-law model for Tmax(N) demonstrates robust convergence and has a physical basis.

Conclusions:

• Accurate extrapolation of the critical temperature (Tc) for the 2D Ising model can be achieved using a limited number of high-precision finite-size results.
• The N/(N+1)-law model offers a robust and physically motivated approach for Tc estimation.
• These findings provide a more efficient and reliable method for determining Tc in statistical physics models.