1995/07/12 by A. Kocic, Aleksandar Kocić, J. B. Kogut +1 · 34 citations
Physics and Astronomy · #Amplitude #Boson #Counterexample #Critical point (mathematics) #High-Energy Particle Collisions Research #Ising model #Mean field theory #Observable #Physics of Superconductivity and Magnetism #Quantum Chromodynamics and Particle Interactions #Renormalization group #Scaling #Universality (dynamical systems) #cond-mat #hep-lat #hep-ph #hep-th #nucl-th
paper · pdf · doi:10.1016/0550-3213(95)00504-l
published in Nuclear Physics B 455(1-2), 229-273 (Elsevier BV) · 47 pages, latex, 23 figures in one uuencoded file
arxiv created 1995/07/12 · openalex publication_date 1995/11/01 · arxiv updated 2015/06/25 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
In a recent Letter we discussed the fact that large-N expansions and computer simulations indicate that the universality class of the finite temperature chiral symmetry restoration transition in the 3D Gross-Neveu model is mean field theory. This was seen to be a counterexample to the standard 'sigma model' scenario which predicts the 2D Ising model universality class. In this article we present more evidence, both theoretical and numerical, that this result is correct. We develop a physical picture for our results and discuss the width of the scaling region (Ginzburg criterion), 1/N corrections, and differences between the dynamics of BCS superconductors and Gross-Neveu models. Lattices as large as 12 × 722 are simulated for both the N=12 and N=4 cases and the numerical evidence for mean field scaling is quite compelling. We point out that the amplitude ratio for the model's susceptibility is a particulartly good observable for distinguishing between the dimensional reduction and the mean field scenerios, because this universal quantity differs by almost a factor of 20 in the two cases. The simulations are done close to the critical point in both the symmetric and broken phases, and correlation lengths of order 10 are measured. The critical indices βmag and δ also pick out mean field behavior. We trace the breakdown of the standard scenario (dimensional reduction and universality) to the composite character of the mesons in the model. We point out that our results should be generic for theories with dynamical symmetry breaking, such as Quantum Chromodynamics. We also simulated the O(2) model on 8 × 163 lattices to establish that our methods give the results of dimensional reduction in purely bosonic