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

J. Engels; F. Karsch; K. Redlich

doi:10.1016/0550-3213(94)00491-V

paper

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

arXiv:hep-lat/9408009 · doi:10.1016/0550-3213(94)00491-V

Abstract

The lattice data for the energy density of $S U (2)$ 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 $I^ I^^{2} -$ 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 $V T^{3}$ with the corresponding $3 d$ Ising model critical exponents. The value of $I^µ (T_{c}) / T_{c}^{4}$ 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.

15 pages + 9 figures, BI-TP 94/30