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Setting Limits on Supersymmetry Using Simplified Models
07:46

Setting Limits on Supersymmetry Using Simplified Models

Published on: November 15, 2013

Majority-vote model on hyperbolic lattices.

Zhi-Xi Wu1, Petter Holme

  • 1Department of Physics, Umeå University, Umeå, Sweden. zhi-xi.wu@physics.umu.se

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|April 7, 2010
PubMed
Summary
This summary is machine-generated.

Critical exponents of the majority-vote model differ on hyperbolic lattices due to effective dimensionality. These exponents satisfy a hyperscaling relation, revealing insights into nonequilibrium statistical models on curved surfaces.

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Area of Science:

  • Statistical Mechanics
  • Complex Systems
  • Non-equilibrium Physics

Background:

  • The majority-vote model is a nonequilibrium statistical model.
  • Regular lattices with periodic boundary conditions often exhibit critical behavior similar to the equilibrium Ising model.
  • Hyperbolic lattices, such as heptagonal and dual heptagonal lattices, can only be embedded in negatively curved surfaces.

Purpose of the Study:

  • To investigate the critical properties of the majority-vote model on heptagonal and dual heptagonal lattices.
  • To compare the critical exponents with those found on regular lattices and other hyperbolic lattices.
  • To understand the influence of effective dimensionality and boundary nodes on the model's ordering process.

Main Methods:

  • Monte Carlo simulations
  • Finite-size analysis
  • Comparative studies of critical exponents

Main Results:

  • Critical exponents (1/nu, beta/nu, gamma/nu) for the majority-vote model on heptagonal and dual heptagonal lattices differ from those on regular lattices.
  • The observed exponents on hyperbolic lattices are also distinct from those of the Ising model on hyperbolic lattices.
  • The critical exponents satisfy the hyperscaling relation 2beta/nu + gamma/nu = D(eff), where D(eff) represents the effective dimension.

Conclusions:

  • The disagreement in critical exponents is attributed to the effective dimensionality of hyperbolic lattices.
  • The hyperscaling relation provides a framework for understanding critical phenomena on these curved surfaces.
  • Boundary nodes can influence the ordering process in the majority-vote model on hyperbolic lattices.