The dynamic exponent of the Ising model on negatively curved surfaces

Abstract

We investigate the dynamic critical exponent of the two-dimensional Ising model defined on a curved surface with constant negative curvature. By using the short-time relaxation method, we find a quantitative alteration of the dynamic exponent from the known value for the planar Ising model. This phenomenon is attributed to the fact that the Ising lattices embedded on negatively curved surfaces act as ones in infinite dimensions, thus yielding the dynamic exponent deduced from mean field theory. We further demonstrate that the static critical exponent for the correlation length exhibits the mean field exponent, which agrees with the existing results obtained from canonical Monte Carlo simulations.

arXiv comment14 pages, 3 figures. to appear in J. Stat. Mech

References in corpus (19)

• 2D Gravity and Random Matrices
• Ageing Properties of Critical Systems
• Generalized Dynamic Scaling for Critical Magnetic Systems
• Topology and the Cosmic Microwave Background
• Dynamic Monte Carlo Measurement of Critical Exponents
• The Dynamic Exponent of the Two-Dimensional Ising Model and Monte Carlo Computation of the Sub-Dominant Eigenvalue of the Stochastic Matrix
• Critical phenomena at perfect and non-perfect surfaces
• Monte Carlo computation of correlation times of independent relaxation modes at criticality
• Dynamic critical behavior of the XY model in small-world networks
• Geometric effects on critical behaviours of the Ising model
• Universality of the Ising Model on Sphere-like Lattices
• Heisenberg spins on a cone: an interplay between geometry and magnetism
• Universal amplitude-exponent relation for the Ising model on sphere-like lattices
• "The Ising model on spherical lattices: dimer versus Monte Carlo approach"
• Ising Spins on a Gravitating Sphere
• Ising Field Theory on a Pseudosphere
• Zero temperature dynamics of Ising model on a densely connected small world network
• Logarithmic corrections to the Ising model free energy on lattices with conical singularities
• Finite-size scaling and conformal anomaly of the Ising model in curved space

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