Estimates of critical quantities from an expansion in mass: Ising model on the simple cubic lattice

TL;DR

This paper introduces a method to estimate critical quantities like temperature and exponents in the 3D Ising model using an expansion in mass and delta-expansion techniques, providing both unbiased and biased estimates.

Contribution

It presents a novel approach to compute critical parameters in the Ising model through a mass expansion and delta-expansion, including estimates of correction-to-scaling exponents.

Findings

Estimated critical inverse temperature $eta_c$ accurately.

Derived critical exponents $ u$, $eta$, $ heta$, and $ ilde{ heta}$.

Validated the method with consistent results for the 3D Ising model.

Abstract

In the Ising model on the simple cubic lattice, we describe the inverse temperature $\beta$ and other quantities relevant for the computation of critical quantities in terms of a dimensionless squared mass $M$. The critical behaviors of those quantities are represented by the linear differential equations with constant coefficients which are related to critical exponents. We estimate the critical temperature and exponents via an expansion in the inverse powers of the mass under the use of $\delta$-expansion. The critical inverse temperature $\beta_{c}$ is estimated first in unbiased manner and then critical exponents are also estimated in biased and unbiased self-contained way including $\omega$, the correction-to-scaling exponent, $\nu$, $\eta$ and $\gamma$.