Complex zeros in the partition function of the four-dimensional SU(2) lattice gauge model

Near the deconfinement transition of SU(2) gauge theory the finite-size scaling behaviour of the order parameter, the susceptibility and the normalized fourth cumulant gr is studied on N,~x N~lattices with N~= 4 and 6 and IV~, = 8, 12, 18, 24 or 26. For that purpose we have calculated new high-statistics data for Nr = 6 and re-evaluated previous results obtained for Nr = 4. In both cases we used the density of states method. We determine the critical coupling and with a new way of phenomenological renormalization the critical exponents. For N. 6 we find that~/g~2 0. 2.4265(30). Using the results for the critical temperature obtained for different N~we examine the approach to asymptotic scaling.

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“…The density of states method was introduced [4][5][6]for partition functions, which may be written in the form…”

Section: The Density Of States Methodsmentioning

confidence: 99%

“…The improvement of the original density of states method [4][5][6]for the evaluation of data [7][8][9]allows now the application of FSS techniques requiring continuous input functions and not only single data points. It seems therefore worthwhile to re-evaluate existing data and to extend the analysis to new data.…”

Section: Introductionmentioning

confidence: 99%

Phenomenological renormalization and scaling behaviour of SU(2) lattice gauge theory

1992

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“…6 shows the susceptibility as a function of β for h = 0.001, calculated on the two largest lattices we have studied. The curves are obtained by interpolating the data points using the density of state method [15]. The Figure clearly indicates that there is no noticeable change of the peak between 700 2 to 1000 2 , so that we are effectively at the infinite volume limit.…”

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confidence: 99%

Cluster percolation and pseudocritical behaviour in spin models

Fortunato

Satz

2001

Physics Letters B

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Abstract:The critical behaviour of many spin models can be equivalently formulated as percolation of specific site-bond clusters. In the presence of an external magnetic field, such clusters remain well-defined and lead to a percolation transition, even though the system no longer shows thermal critical behaviour. We investigate the 2-dimensional Ising model and the 3-dimensional O(2) model by means of Monte Carlo simulations. We find for small fields that the line of percolation critical points has the same functional form as the line of thermal pseudocritical points.Percolation theory [1,2] provides in many cases an elegant interpretation of the mechanism of second order phase transitions: the existence of an infinite spanning cluster represents the new order of the microscopic constituents of the system due to spontaneous symmetry breaking.In the Ising model, a rigorous correspondence between thermal critical behaviour and percolation was established by Coniglio and Klein [3]; the clusters are constructed by linking like-sign spins through a temperature-dependent bond probability p = 1 − exp(−2J/kT ), where J is the Ising coupling and T the temperature. This result has been recently extended to a wide class of models, from continuous spin Ising-like models [4,5] to O(n) models [6]. In all cases the system was considered in the absence of any external field. The reason for this is clear: by introducing an external field H, we explicitly break the symmetry of the Hamiltonian of the system, thus eliminating the thermal critical behaviour of the model. None of the thermodynamic potentials exhibits discontinuities of any kind, since the partition function is analytical for H = 0.On the other hand, the Coniglio-Klein clusters can be built as well when H =0. Because of the field, the system has a non-vanishing magnetization m parallel to the direction of H for any finite value of the temperature T . For T → ∞, m→ 0, and for T = 0, m = 1. This suggests that for a fixed value of H, the clusters will start to form an infinite network at some temperature T p (H). Varying the field H, one thus obtains a curve T p (H) in the T − H plane, the Kertész line [7].The Kertész line specifies the usual percolation threshold, just as in the case H = 0, and the percolation variables exibit the usual singularities, leading to a set of critical exponents. In particular, the percolation strength, which is the relative size of the percolation cluster compared to the total volume of the system, remains the order parameter of the percolation transition.

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“…Clearly we would like to go beyond pure N = 1 super-Yang-Mills, and in fact all other models contain scalar fields-which are the source of many difficulties due to unwanted renormalizations that cannot be forbidden by symmetries. Recently it was proposed [19] that an acceptable amount of fine-tuning could be efficiently performed using a multicanonical Monte Carlo [20] simulation together with Ferrenberg-Swendsen reweighting [21][22][23] in a large class of theories; see also [9]. In any such program, it is necessary to study the divergence of the supercurrent and its renormalization, such as we are doing here for the Wess-Zumino model.…”

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confidence: 99%

Supercurrent conservation in the lattice Wess-Zumino model with Ginsparg-Wilson fermions

2011

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We study supercurrent conservation for the four-dimensional Wess-Zumino model formulated on the lattice. The formulation is one that has been discussed several times, and uses Ginsparg-Wilson fermions of the overlap (Neuberger) variety, together with an auxiliary fermion (plus superpartners), such that a lattice version of U (1) R symmetry is exactly preserved in the limit of vanishing bare mass. We show that the almost naive supercurrent is conserved at one loop. By contrast we find that this is not true for Wilson fermions and a canonical scalar action. We provide nonperturbative evidence for the nonconservation of the supercurrent in Monte Carlo simulations.

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Complex zeros in the partition function of the four-dimensional SU(2) lattice gauge model

Cited by 173 publications

References 4 publications

Phenomenological renormalization and scaling behaviour of SU(2) lattice gauge theory

Phenomenological renormalization and scaling behaviour of SU(2) lattice gauge theory

Cluster percolation and pseudocritical behaviour in spin models

Supercurrent conservation in the lattice Wess-Zumino model with Ginsparg-Wilson fermions

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