The Interface Tension of the Three-dimensional Ising Model in Two-loop Order

TL;DR

This paper calculates the universal dimensionless interface tension product for the 3D Ising model using two-loop field theory corrections, aligning well with experimental and simulation data.

Contribution

It provides a two-loop order calculation of the universal interface tension product in the 3D Ising model using field theory.

Findings

Calculated R_- = 0.1065(9) with two-loop corrections.

Results agree with experimental and Monte Carlo data.

Refined the theoretical estimate of interface tension in 3D systems.

Abstract

In liquid mixtures and other binary systems at low temperatures the pure phases may coexist, separated by an interface. The interface tension vanishes according to $\sigma = \sigma_0 (1 - T/T_c)^{\mu}$ as the temperature T approaches the critical point from below. Similarly the correlation length diverges as $\xi = f_- (1 - T/T_c)^{-\nu}$ in the low temperature region. For three-dimensional systems the dimensionless product $R_- = \sigma_0 f_-^2$ is universal. We calculate its value in the framework of field theory in d=3 dimensions by means of a saddle-point expansion around the kink solution including two-loop corrections. The result R_ = 0.1065(9), where the error is mainly due to the uncertainty in the renormalized coupling constant, is compatible with experimental data and Monte Carlo calculations.