2004/07/12 by Yoshihiro Nishiyama
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Complex Network Analysis Techniques #Complex Systems and Time Series Analysis #Condensed matter physics #Critical exponent #Criticality #Crossover #Exponent #Geometry #Ising model #Mathematical physics #Mathematics #Monte Carlo method #Phase transition #Physics #Renormalization group #Scaling #Statistical physics #Statistics #Theoretical and Computational Physics #Transfer matrix #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.70.026120
published as Phys. Rev. E 70, 026120 (2004).
arxiv created 2004/07/12 · openalex publication_date 2004/08/31 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
A three-dimensional Ising model with the plaquette-type (next-nearest-neighbor and four-spin) interactions is investigated numerically. This extended Ising model, the so-called gonihedric model, was introduced by Savvidy and Wegner as a discretized version of the interacting (closed) surfaces without surface tension. The gonihedric model is notorious for its slow relaxation to the thermal equilibrium (glassy behavior), which deteriorates the efficiency of the Monte Carlo sampling. We employ the transfer-matrix (TM) method, implementing Novotny's idea, which enables us to treat an arbitrary number of spins N for one TM slice even in three dimensions. This arbitrariness admits systematic finite-size-scaling analyses. Accepting the extended parameter space by Cirillo et al., we analyzed the (multi-) criticality of the gonihedric model for N</=13. Thereby, we found that, as first noted by Cirillo et al. analytically (cluster-variation method), the data are well described by the multicritical (crossover) scaling theory. That is, the previously reported nonstandard criticality for the gonihedric model is reconciled with a crossover exponent and the ordinary three-dimensional-Ising universality class. We estimate the crossover exponent and the correlation-length critical exponent at the multicritical point as phi=0.6(2) and nu; =0.45(15), respectively.