Nonstandard Finite-Size Scaling at First-Order Phase Transitions

We show that the standard inverse system volume scaling for finite-size corrections at a first-order phase transition (i.e., $1/L^3$ for an $L \times L \times L$ lattice in $3D$) is transmuted to $1/L^2$ scaling if there is an exponential low-temperature phase degeneracy. The gonihedric Ising model which has a four-spin interaction, plaquette Hamiltonian provides an exemplar of just such a system. We use multicanonical Monte Carlo simulations of this model to generate high-precision data which provides strong confirmation of the nonstandard finite-size scaling law. The dual to the gonihedric model, which is an anisotropically coupled Ashkin-Teller model, has a similar degeneracy and also displays the nonstandard scaling behavior. Further potential applications of the transmuted finite-size scaling law will be briefly discussed.\\[1mm] M. Mueller, W. Janke, D.A. Johnston, Phys. Rev. Lett. {\bf 112} (2014) 200601; M. Mueller, D.A. Johnston, W. Janke, Nucl. Phys. B {\bf 888} (2014) 214.