Delta expansion at low temperatures

TL;DR

This paper investigates the critical behavior of the inverse temperature in the low-temperature phase of the square Ising model using delta-expansion and differential equations to accurately estimate the critical inverse temperature.

Contribution

It introduces a novel application of delta-expansion combined with differential equations to improve critical temperature estimation in the Ising model.

Findings

Accurate estimation of critical inverse temperature beta_c.

Effective use of delta-expansion for scaling behavior.

Improved correction exponent estimation enhances results.

Abstract

In the low temperature phase of the square Ising model, we describe the inverse temperature beta as the function of a squared mass M and study the critical behavior of beta(M) via the large M expansion. Using the delta-expansion by which the large mass expansion is transformed into a series exhibiting expected scaling behavior, we perform the estimation of the critical inverse temperature beta_{c} with the help of linear differential equation to be satisfied by ansatz of beta(M) near the critical point M=0. To improve the estimation, the leading correction exponent nu is independently estimated from beta^{(2)}/beta^{(1)} and is used in the estimation of beta_{c}, giving rise to remarkable accuracy improvement.