Critical behaviors as functions of the bare-mass

TL;DR

This paper investigates the critical behavior of the inverse temperature in the 3D Ising model as a function of bare-mass, using delta expansion and parameter optimization to accurately estimate the critical temperature and exponent.

Contribution

It introduces a method to improve critical point estimation by suppressing correction terms through derivative adjustments and the principle of minimum sensitivity.

Findings

Estimated critical inverse temperature _c in good agreement with known values.

Accurately estimated the critical exponent .

Demonstrated effectiveness of derivative parameter optimization in critical behavior analysis.

Abstract

In Ising model on the simple cubic lattice, we describe the inverse temperature \beta in terms of the bare-mass M and study its critical behavior by the use of delta expansion from high temperature or large M side. In the vicinity of critical temperature \beta_{c}, the expansion of \beta in M has \beta_{c} as the first term and M^{-1/2\nu} as the leading correction. The estimation of \beta_{c} in 1/M expansion is confronted with the leading and higher order corrections, even delta expansion is applied and the critical region emerges. To improve the estimation status of \beta_{c}, we try to suppress the corrections by adding derivatives of \beta(M) with free adjustable parameters. By optimizing the parameters with the help of the principle of minimum sensitivity which are maximally imposed in accord with the number of parameters, estimation of \beta_{c} is carried out and the result is found to be in good agreement with the present world average. In the same time, the critical exponent {\nu} is also estimated.