Low-Temperature Series for the Correlation Length in $d=3$ Ising Model

TL;DR

This paper extends low-temperature series for the 3D Ising model's correlation length and susceptibility, providing refined estimates of critical exponents through series analysis.

Contribution

It introduces extended low-temperature series for the correlation function and correlation length in the 3D Ising model, improving critical exponent estimates.

Findings

Critical exponents estimated as 2ν'+γ' ≈ 2.55

Correlation length series extended to u^{23}

Enhanced understanding of phase transition behavior

Abstract

We extend low-temperature series for the second moment of the correlation function in $d=3$ simple-cubic Ising model from $u^{15}$ to $u^{26}$ using finite-lattice method, and combining with the series for the susceptibility we obtain the low-temperature series for the second-moment correlation length to $u^{23}$. An analysis of the obtained series by inhomogeneous differential approximants gives critical exponents $ 2\nu^{\prime} + \gamma^{\prime} \approx 2.55 $ and $ 2\nu^{\prime} \approx 1.27 $.