Scaling Properties of the Energy Density in SU(2) Lattice Gauge Theory

TL;DR

This paper investigates the scaling behavior of energy density in SU(2) lattice gauge theory near the critical temperature, demonstrating consistency with 3D Ising model exponents and estimating the continuum limit value.

Contribution

It provides a detailed finite size scaling analysis of the energy density in SU(2) gauge theory and estimates the critical energy density in the continuum limit.

Findings

Energy density scales with $VT^3$ at $T_c$ following 3D Ising exponents.

Estimated $rac{\e(T_c)}{T_c^4}$ in the continuum limit is 0.256(23).

At twice the critical temperature, energy density reaches about 70% of the weak coupling limit.

Abstract

The lattice data for the energy density of $SU(2)$ gauge theory are calculated with \nop~derivatives of the coupling constants. These derivatives are obtained from two sources : i) a parametrization of the \nop~beta function in accord with the measured critical temperature and $\Delta\beta-$values and ii) a \nop~calculation of the presssure. We then perform a detailed finite size scaling analysis of the energy density near $T_c$. It is shown that at the critical temperature the energy density is scaling as a function of $VT^3$ with the corresponding $3d$ Ising model critical exponents. The value of $\epsilon(T_c)/T^4_c$ in the continuum limit is estimated to be 0.256(23). In the high temperature regime the energy density is approaching its weak coupling limit from below, at $T/T_c \approx 2$ it has reached only about $70\%$ of the limit.