Critical behaviour of the Ising model on the 4-dimensional lattice

Abstract

In this paper we investigate the nature of the singularity of the Ising model of the 4-dimensional cubic lattice. It is rigorously known that the specific heat has critical exponent $\alpha =0$ but a non-rigorous field-theory argument predicts an unbounded specific heat with a logarithmic singularity at $T_c$. We find that within the given accuracy the canonical ensemble data is consistent both with a logarithmic singularity and a bounded specific heat, but that the micro-canonical ensemble lends stronger support to a bounded specific heat. Our conclusion is that either much larger system sizes are needed for Monte Carlo studies of this model in four dimensions or the field theory prediction of a logarithmic singularity is wrong.

5 pages, 7 figures

References in corpus (1)

• High-temperature series for the bond-diluted Ising model in 3, 4 and 5 dimensions

Cited by in corpus (28)

• Interaction effects and quantum phase transitions in topological insulators
• Using Superconducting Qubit Circuits to Engineer Exotic Lattice Systems
• Non-vanishing boundary effects and quasi-first order phase transitions in high dimensional Ising models
• The high-temperature expansions of the higher susceptibilities for the Ising model in general dimension d
• Applicability of n-vicinity method for calculation of free energy of Ising model
• Anomalous mean-field behavior of the fully connected Ising model
• Magnetisation and mean field theory in the Ising model
• Analytical solutions for Ising models on high dimensional lattices
• Experimental signals for a second resonance of the Higgs field
• Logarithmic finite-size scaling of the self-avoiding walk at four dimensions
• The mass scales of the Higgs field
• Dependence of critical parameters of 2D Ising model on lattice size
• ${\mathbb{Z}}_2$ Lattice Gerbe Theory
• Model of Fractionalization of Faraday Lines in Compact Electrodynamics
• Revising the universality class of the four-dimensional Ising model
• Dipolar ordering transitions in many-body quantum optics: Analytical diagrammatic approach to equilibrium quantum spins
• Dynamics of a lattice 2-group gauge theory model
• Magnetization profiles at the upper critical dimension as solutions of the integer Yamabe problem
• Lifted directed-worm algorithm
• Logarithmic Finite-Size Scaling of the Four-Dimensional Ising Model
• Second resonance of the Higgs field: motivations, experimental signals, unitarity constraints
• Quantum Non-Locality and the CMB: what Experiments say
• Statistical mechanics approach to lattice field theory
• Phase transitions in voting simulated by an intelligent Ising model
• Characterizing spin ordering via maximal row correlation in classical spin models
• N-vicinities method for 3D Ising Model
• The Analytical Expressions for a Finite-Size 2D Ising Model
• Two stroke Pumping Technique for Many-Body Systems