Transmuted finite-size scaling at first-order phase transitions

Abstract

It is known that fixed boundary conditions modify the leading finite-size corrections for an L^3 lattice in 3d at a first-order phase transition from 1/L^3 to 1/L. We note that an exponential low-temperature phase degeneracy of the form 2^3L will lead to a different leading correction of order 1/L^2 . A 3d gonihedric Ising model with a four-spin interaction, plaquette Hamiltonian displays such a degeneracy and we confirm the modified scaling behaviour using high-precision multicanonical simulations. We remark that other models such as the Ising antiferromagnet on the FCC lattice, in which the number of "true" low-temperature phases is not macroscopically large but which possess an exponentially degenerate number of low lying states may display an effective version of the modified scaling law for the range of lattice sizes accessible in simulations.

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Cited by in corpus (5)

• Plaquette Ising models, degeneracy and scaling
• Finite-size scaling of Monte Carlo simulations for the fcc Ising antiferromagnet: Effects of the low-temperature phase degeneracy
• Planar ordering in the plaquette-only gonihedric Ising model
• (Four) Dual Plaquette 3D Ising Models
• Macroscopic Degeneracy and order in the 3d plaquette Ising model