Revising the universality class of the four-dimensional Ising model

Abstract

The aim of this paper is to determine the behavior of the specific heat of the 4-dimensional Ising model at the critical temperature, and via that determine if the Ising model and the ${\varphi }^4$-model belong to the same universality class in dimension 4. In order to do this we have carried out what is currently the largest scale simulations of the 4-dimensional Ising model, extending the lattices size up to $L=256$ and the number of samples per size by several orders of magnitude compared to earlier works, keeping track of data for both the canonical and microcanonical ensembles. Our conclusion is that the Ising model has a bounded specific heat, while the ${\varphi }^4$-model is known to have a logarithmic divergence at the critical point. Hence the two models belong to distinct universality classes in dimension 4.

16 pages, 30 figures

References in corpus (7)

• Equivalence and nonequivalence of ensembles: Thermodynamic, macrostate, and measure levels
• Critical behaviour of the Ising model on the 4-dimensional lattice
• Non-vanishing boundary effects and quasi-first order phase transitions in high dimensional Ising models
• The discontinuity of the specific heat for the 5D Ising model
• High-temperature series for the bond-diluted Ising model in 3, 4 and 5 dimensions
• The mass scales of the Higgs field
• A hidden, heavier resonance of the Higgs field

Cited by in corpus (4)

• Revisiting the Lee-Yang singularities in the four-dimensional Ising model: a tribute to the memory of Ralph Kenna
• Triad representation for the anisotropic tensor renormalization group in four dimensions
• Logarithmic Finite-Size Scaling of the Four-Dimensional Ising Model
• Second resonance of the Higgs field: motivations, experimental signals, unitarity constraints