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

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 $\gamma$.