We consider the hard-core model on a finite square grid graph with stochasticGlauber dynamics parametrized by the inverse temperature $\beta$. Weinvestigate how the transition between its two maximum-occupancy configurationstakes place in the low-temperature regime $\beta\to\infty$ in the case ofperiodic boundary conditions. The hard-core constraints and the grid symmetrymake the structure of the critical configurations, also known as essentialsaddles, for this transition very rich and complex. We provide a comprehensivegeometrical characterization of the set of critical configurations that areasymptotically visited with probability one. In particular, we develop a novelisoperimetric inequality for hard-core configurations with a fixed number ofparticles and we show how not only their size but also their shape determinesthe characterization of the saddles.
Critical configurations of the hard-core model on square grid graphs
Simone Baldassarri
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2025-01-01
Abstract
We consider the hard-core model on a finite square grid graph with stochasticGlauber dynamics parametrized by the inverse temperature $\beta$. Weinvestigate how the transition between its two maximum-occupancy configurationstakes place in the low-temperature regime $\beta\to\infty$ in the case ofperiodic boundary conditions. The hard-core constraints and the grid symmetrymake the structure of the critical configurations, also known as essentialsaddles, for this transition very rich and complex. We provide a comprehensivegeometrical characterization of the set of critical configurations that areasymptotically visited with probability one. In particular, we develop a novelisoperimetric inequality for hard-core configurations with a fixed number ofparticles and we show how not only their size but also their shape determinesthe characterization of the saddles.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
