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- W3092827732 abstract "We construct finite-range interactions on $mathcal{S}^{mathbb{Z}^2}$, where $mathcal{S}$ is a finite set, for which the associated equilibrium states (i.e., the shift-invariant Gibbs states) fail to converge as temperature goes to zero. More precisely, if we pick any one-parameter family $(mu_beta)_{beta>0}$ in which $mu_beta$ is an equilibrium state at inverse temperature $ beta$ for this interaction, then $lim_{betatoinfty}mu_beta$ does not exist. This settles a question posed by the first author and Hochman who obtained such a non-convergence behavior when $dgeq 3$, $d$ being the dimension of the lattice." @default.
- W3092827732 created "2020-10-22" @default.
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- W3092827732 date "2020-10-18" @default.
- W3092827732 modified "2023-09-27" @default.
- W3092827732 title "On the absence of zero-temperature limit of equilibrium states for finite-range interactions on the lattice $mathbb{Z}^2$" @default.
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- W3092827732 hasPublicationYear "2020" @default.
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