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| Format: | Preprint |
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2026
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| Online Access: | https://arxiv.org/abs/2605.12708 |
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| _version_ | 1866916006891356160 |
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| author | Attali, Jean-Gabriel |
| author_facet | Attali, Jean-Gabriel |
| contents | For the low-temperature two-dimensional Ising model, the two pure Gibbs phases exhaust the extremal equilibrium states, but not the pathwise absorbing structure of the Glauber dynamics. Let \[ P^\pm=\{σ:M_n(σ)\to \pm m_β\},\qquad R=Ω\setminus(P^+\cup P^-). \] We show that \(R\) is null under both pure phases but contains a dense pathwise confined subset. More precisely, we construct a dense family of initial configurations whose trajectories are confined to the centered sector \[ C_0=\{σ:M_n(σ)\to0\}\subset R. \] Nevertheless, the corresponding Cesaro averages converge to \(\frac12(μ^++μ^-)\). Thus the pathwise absorbing geometry is richer than the Gibbs-phase classification, without creating a third Gibbs phase. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_12708 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Equilibrium Biphasicity and Non-Binary Pathwise Confinement in Stochastic Ising Models Attali, Jean-Gabriel Probability Mathematical Physics 60K35 For the low-temperature two-dimensional Ising model, the two pure Gibbs phases exhaust the extremal equilibrium states, but not the pathwise absorbing structure of the Glauber dynamics. Let \[ P^\pm=\{σ:M_n(σ)\to \pm m_β\},\qquad R=Ω\setminus(P^+\cup P^-). \] We show that \(R\) is null under both pure phases but contains a dense pathwise confined subset. More precisely, we construct a dense family of initial configurations whose trajectories are confined to the centered sector \[ C_0=\{σ:M_n(σ)\to0\}\subset R. \] Nevertheless, the corresponding Cesaro averages converge to \(\frac12(μ^++μ^-)\). Thus the pathwise absorbing geometry is richer than the Gibbs-phase classification, without creating a third Gibbs phase. |
| title | Equilibrium Biphasicity and Non-Binary Pathwise Confinement in Stochastic Ising Models |
| topic | Probability Mathematical Physics 60K35 |
| url | https://arxiv.org/abs/2605.12708 |