On the Truncation of Systems with Non-Summable Interactions

2005/04/28 by S. Friedli, Sacha Friedli, Bernardo N. B. de Lima +1
Mathematics · Physics and Astronomy · #Combinatorics #Computer science #Condensed matter physics #Integer (computer science) #Inverse #Inverse temperature #Ising model #Markov Chains and Monte Carlo Methods #Mathematical physics #Mathematics #Percolation (cognitive psychology) #Physics #Potts model #Simple (philosophy) #Spins #Statistical physics #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #Thermodynamics #Truncation (statistics) #cond-mat.stat-mech

paper · pdf · doi:10.1007/s10955-005-8023-9

18 pages, 4 figures

arxiv created 2005/04/28 · openalex publication_date 2006/03/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

In this note we consider long range q-states Potts models on Z^d, d≥ 2. For various families of non-summable ferromagnetic pair potentials ϕ(x)≥ 0, we show that there exists, for all inverse temperature β>0, an integer N such that the truncated model, in which all interactions between spins at distance larger than N are suppressed, has at least q distinct infinite-volume Gibbs states. This holds, in particular, for all potentials whose asymptotic behaviour is of the type ϕ(x)∼ ‖x‖^-α, 0≤α≤ d. These results are obtained using simple percolation arguments.

Citations

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