Spectral density study of the SU(3) deconfining phase transition

Abstract

We present spectral density reweighting techniques adapted to the analysis of a time series of data with a continuous range of allowed values. In a first application we analyze action and Polyakov line data from a Monte Carlo simulation on L t L 3 (L t = 2, 4) lattices for the SU(3) deconfining phase transition. We calculate partition function zeros, as well as maxima of the specific heat and of the order parameter susceptibility. Details and warnings are given concerning i) autocorrelations in computer time and ii) a reliable extraction of partition function † Submitted to Nuclear 1 zeros. The finite size scaling analysis of these data leads to precise results for the critical couplings β c , for the critical exponent ν and for the latent heat △s. In both cases (L t = 2 and 4), the first order nature of the transition is substantiated.

Approximate forms of the density of states in pure gauge theory

“…In this contour plot, the outer contours go through the bins that have 20 zeros, the first inner contours correspond to 60 zeros, the next to 100 zeros etc.. The circle of confidence [8] in the Gaussian approximation for 40,000 independent configurations as well as another estimate (red boxes in Fig. 2) of the region of confidence discussed in [10] are shown on this graph for reference.…”

“…In particular, it can be used to determine the Fisher's zeros of the partition function [7,8]. Locating these zeros in the complex β plane and their volume dependence is important to understand the large order behavior of the weak coupling expansion [4,9,10,11] at zero temperature and the nature of the finite temperature transition [12].…”

Fisher's Zeros and Perturbative Series in Gluodynamics

“…1, the distribution of values of S for SU (2) can be fitted very well with a Gaussian with σ 2 S =< S 2 > − < S > 2 . This suggests [20] a criterion to determine a region of confidence for MC zeros. For a Gaussian distribution, the fluctuation in exp(−∆β (S− < S >)) is smaller than the average for |∆β | 2 < ln(N con f .…”

Structural transitions in biomolecules - a numerical comparison of two approaches for the study of phase transitions in small systems

“…[18] and references therein). In Table 1 we present our first four partition function zeros, although the fourth one is less reliable due to the presence of fake zeros [19]. Using these zeros we first calculated the parameters α u and γ u which characterize in the Borrmann et al approach phase transitions in small systems.…”