2011/06/23 by D.A. Johnston, Johnston, D. A., Ranasinghe, R. P. K. C. M.
Mathematics · Physics and Astronomy · #FOS: Physical sciences #Markov Chains and Monte Carlo Methods #Quantum many-body systems #Statistical Mechanics (cond-mat.stat-mech) #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.1106.4664
openalex publication_date 2011/06/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We note that two formulations of dual gonihedric Ising models in 3d, one based on using Wegner's general framework for duality to construct a dual Hamiltonian for codimension one surfaces, the other on constructing a dual Hamiltonian for two-dimensional surfaces, are related by a variant of the standard decoration/iteration transformation. The dual Hamiltonian for two-dimensional surfaces contains a mixture of link and vertex spins and as a consequence possesses a gauge invariance which is inherited by the codimension one surface Hamiltonian. This gauge invariance ensures the latter is equivalent to a third formulation, an anisotropic Ashkin-Teller model. We describe the equivalences in detail and discuss some Monte-Carlo simulations which support these observations.