Zero-temperature dynamics of 2D and 3D Ising ferromagnets

Palani Sundaramurthy, D. L. Stein

    Research output: Contribution to journalArticle

    Abstract

    We consider zero-temperature, stochastic Ising models σt with nearest-neighbour interactions in two and three dimensions. Using both symmetric and asymmetric initial configurations σ0, we study the evolution of the system with time. We examine the issue of convergence of σt and discuss the nature of the final state of the system. By determining a relation between the median number of spin flips per site ν, the probability p that a spin in the initial spin configuration takes the value +1, and lattice size L, we conclude that in two and three dimensions, the system converges to a frozen (but not necessarily uniform) state when p ≠ 1/2. Results for p = 1/2 in three dimensions are consistent with the conjecture that the system does not evolve towards a fully frozen limiting state. Our simulations also uncover 'striped' and 'blinker' states first discussed by Spirin et al (2001 Phys. Rev. E 63 036118), and their statistical properties are investigated.

    Original languageEnglish (US)
    Pages (from-to)349-362
    Number of pages14
    JournalJournal of Physics A: Mathematical and General
    Volume38
    Issue number2
    DOIs
    StatePublished - Jan 14 2005

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    Ising model
    Ferromagnet
    Ising
    Three-dimension
    Zero
    Two Dimensions
    Stochastic Ising Model
    configurations
    Temperature
    Configuration
    temperature
    Flip
    Statistical property
    Nearest Neighbor
    Limiting
    Converge
    simulation
    Interaction
    interactions
    Simulation

    ASJC Scopus subject areas

    • Mathematical Physics
    • Physics and Astronomy(all)
    • Statistical and Nonlinear Physics

    Cite this

    Zero-temperature dynamics of 2D and 3D Ising ferromagnets. / Sundaramurthy, Palani; Stein, D. L.

    In: Journal of Physics A: Mathematical and General, Vol. 38, No. 2, 14.01.2005, p. 349-362.

    Research output: Contribution to journalArticle

    Sundaramurthy, Palani ; Stein, D. L. / Zero-temperature dynamics of 2D and 3D Ising ferromagnets. In: Journal of Physics A: Mathematical and General. 2005 ; Vol. 38, No. 2. pp. 349-362.
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