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

• 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 -partial derivative S-2/partial derivative U-2. 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.

Ämnesord

NATURVETENSKAP  -- Fysik (hsv//swe)

NATURAL SCIENCES  -- Physical Sciences (hsv//eng)

Nyckelord

Ising model

Phase transitions

Boundary effects

Physics

Fysik

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