Universality in Generalized Ising Models

Jan H. Meinke, Phillip M. Duxbury

Hong-Ming Cui, Zhong-Ying Fan

A bstract The symmetry of Ising model questions any single crossover scenario for supercritical fluids. In this work, we firstly study a pair of thermodynamic crossovers L ± analytically for the Van der Waals class fluids. We uncover an emergent Z 2 symmetry in addition to the universal scalings in the scaling regime for this class fluids. By using the self-reciprocal property between coexistenct phases, we further establish that under suitable conditions, the Ising symmetry generally emerges in the scaling regime for a general universality class. As a consequence, the thermodynamic crossovers L ± generally exhibit an emergent Z 2 symmetry in the scaling regime. This partly resolves the symmetry puzzle raised by the Ising model. The results also imply that the physical importance of the Ising model in critical phenomenon is far beyond the scope of magentic transitions.

Kazuyuki Matsumoto, Yuko Akutsu

This paper investigates the generalized McCoy-Wu type random Ising model. It is found that boundary magnetization behaves as (Tc − T)β', β' = 1 just below the critical temperature. From numerical analyses it is revealed that this type of critical behavior, β' = 1, is universal for any type of randomness. This universal behavior is explained in terms of the destruction of the devil's staircase structure.

Vieri Mastropietro

M. Van den Nest, Wolfgang Dür, Hans J. Briegel

We prove that the 2D Ising model is complete in the sense that the partition function of any classical q-state spin model (on an arbitrary graph) can be expressed as a special instance of the partition function of a 2D Ising model with complex inhomogeneous couplings and external fields. In the case where the original model is an Ising or Potts-type model, we find that the corresponding 2D square lattice requires only polynomially more spins with respect to the original one, and we give a constructive method to map such models to the 2D Ising model. For more general models the overhead in system size may be exponential. The results are established by connecting classical spin models with measurement-based quantum computation and invoking the universality of the 2D cluster states.

M. P. Nightingale, Henk W. J. Blöte