The discontinuity of the specific heat for the 5D Ising model

Abstract

In this paper we investigate the behaviour of the specific heat around the critical point of the Ising model in dimension 5 to 7. We find a specific heat discontinuity, like that for the mean field Ising model, and provide estimates for the left and right hand limits of the specific heat at the critical point. We also estimate the singular exponents, describing how the specific heat approaches those limits. Additionally, we make a smaller scale investigation of the same properties in dimension 6 and 7, and provide strongly improved estimates for the critical termperature $K_c$ in $d=5,6,7$ which bring the best MC-estimate closer to those obtained by long high temperature series expanions.

8 pages, 13 figures

References in corpus (6)

• Mean-field behavior for long- and finite range Ising model, percolation and self-avoiding walk
• Non-vanishing boundary effects and quasi-first order phase transitions in high dimensional Ising models
• Finite size scaling of the 5D Ising model with free boundary conditions
• The high-temperature expansions of the higher susceptibilities for the Ising model in general dimension d
• Extended Scaling in High Dimensions
• Complete graph asymptotics for the Ising and random cluster models on 5D grids with cyclic boundary

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• Dependence of critical parameters of 2D Ising model on lattice size
• Boundary effects on finite-size scaling for the 5-dimensional Ising model
• Revising the universality class of the four-dimensional Ising model
• Finite-Size Scaling of the High-Dimensional Ising Model in the Loop Representation
• The Analytical Expressions for a Finite-Size 2D Ising Model