Critical behaviour of SU(2) lattice gauge theory. A complete analysis with the χ2-method

Abstract

We determine the critical point and the ratios β/ν and γ/ν of critical exponents of the deconfinement transition in SU (2) gauge theory by applying the χ 2 -method to Monte Carlo data of the modulus and the square of the Polyakov loop. With the same technique we find from the Binder cumulant g r its universal value at the critical point in the thermodynamical limit to −1.403(16) and for the next-to-leading exponent ω = 1 ± 0.1. From the derivatives of the Polyakov loop dependent quantities we estimate then 1/ν. The result from the derivative of g r is 1/ν = 0.63 ± 0.01, in complete agreement with that of the 3d Ising model.

Percolation and deconfinement in SU(2) gauge theory

“…This was conjectured on the basis of effective theories [5,6] and confirmed by lattice studies [7]. The order parameter for SU(2) is the lattice average of the Polyakov loop, and it behaves like the magnetization in the Ising model; in particular, the critical exponents are the same.…”

“…In particular, in case of second order phase transitions, both models would belong to the same universality class, that is they would have the same set of critical exponents. One simple test of the Svetitsky-Yaffe conjecture is provided by the SU(2) gauge theory: numerical simulations showed that its critical exponents indeed coincide with the ones of the Ising model [7].…”

Nf = 1 QCD simulation with improved gauge action at finite temperature

“…For Eq. (6) ω was fixed to 1 in accordance with [8]. As an example in Fig.2 This might be due to less statistics.…”

“…In this study we use χ 2 -method [8] to find critical β for each κ. By differentiating the singular part of the free energy density on N 3 s × N t lattice and expanding these equations with respect to x, we obtain the leading N s behavior at x = 0, Table 1 n and Acc are the number of degrees of polynomial and acceptance ratio of the HMC respectively.…”

“…The critical point can be obtained at the point where a fit to the leading N s -behavior has the least χ 2 [8].…”