Non-vanishing boundary effects and quasi-first order phase transitions in high dimensional Ising models

Abstract

In order to gain a better understanding of the Ising model in higher dimensions we have made a comparative study of how the boundary, open versus cyclic, of a d-dimensional simple lattice, for d=1,...,5, affects the behaviour of the specific heat C and its microcanonical relative, the entropy derivative -dS/dU. In dimensions 4 and 5 the boundary has a strong effect on the critical region of the model and for cyclic boundaries in dimension 5 we find that the model displays a quasi first order phase transition with a bimodal energy distribution. The latent heat decreases with increasing systems size but for all system sizes used in earlier papers the effect is clearly visible once a wide enough range of values for K is considered. Relations to recent rigorous results for high dimensional percolation and previous debates on simulation of Ising models and gauge fields are discussed.

arXiv comment12 pages, 27 figures

References in corpus (11)

• On the Number of Incipient Spanning Clusters
• An Introduction to the Thermodynamic and Macrostate Levels of Nonequivalent Ensembles
• Critical behaviour of the Ising model on the 4-dimensional lattice
• Finite-size scaling above the upper critical dimension revisited: The case of the five-dimensional Ising model
• Universality and the five-dimensional Ising model
• Random graph asymptotics on high-dimensional tori. II. Volume, diameter and mixing time
• Finite-Size Effects in the ${\varphi }^4$ Field Theory Above the Upper Critical Dimension
• Lattice ${\varphi }^4$ theory of finite-size effects above the upper critical dimension
• Comparison of perturbative RG theory with lattice data for the 4d Ising model
• Repairing Stevenson's step in the 4d Ising model
• First lattice evidence for a non-trivial renormalization of the Higgs condensate

Cited by in corpus (28)

• Hyperscaling above the upper critical dimension
• Phase transition of four-dimensional Ising model with higher-order tensor renormalization group
• On the role of Fourier modes in finite-size scaling above the upper critical dimension
• Finite size scaling of the 5D Ising model with free boundary conditions
• A new critical exponent koppa and its logarithmic counterpart koppa-hat
• Geometric explanation of anomalous finite-size scaling in high dimensions
• The discontinuity of the specific heat for the 5D Ising model
• Universal Finite-Size Scaling for Percolation Theory in High Dimensions
• Phase transition of four-dimensional lattice ${\varphi }^4$ theory with tensor renormalization group
• The scaling window of the 5D Ising model with free boundary conditions
• The length of self-avoiding walks on the complete graph
• Triviality problem and the high-temperature expansions of the higher susceptibilities for the Ising and the scalar field models on four-, five- and six-dimensional lattices
• Experimental signals for a second resonance of the Higgs field
• Complete graph asymptotics for the Ising and random cluster models on 5D grids with cyclic boundary
• The mass scales of the Higgs field
• Logarithmic finite-size scaling of the self-avoiding walk at four dimensions
• Phase transition of four-dimensional Ising model with tensor network scheme
• Boundary effects on finite-size scaling for the 5-dimensional Ising model
• Revising the universality class of the four-dimensional Ising model
• Effective-Dimension Theory of Critical Phenomena above Upper Critical Dimensions
• The fifty-year quest for universality in percolation theory in high dimensions
• Two-point functions of random-length random walk on high-dimensional boxes
• Second resonance of the Higgs field: motivations, experimental signals, unitarity constraints
• Quantum Non-Locality and the CMB: what Experiments say
• When correlations exceed system size: finite-size scaling in free boundary conditions above the upper critical dimension
• First-order transition in the stacked-$J_1$-$J_2$ Ising model on a cubic lattice
• On a previously unpublished work with Ralph Kenna
• The Ising ferromagnet in dimension five: link and spin overlaps