 05434 Marek Biskup and Roman Kotecky
 Phase coexistence of gradient Gibbs states
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Dec 21, 05

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Abstract. We consider the (scalar) gradient fields $\eta=(\eta_b)$with $b$ denoting the nearestneighbor edges in $\Z^2$that are distributed according to the Gibbs measure proportional to $\texte^{\beta H(\eta)}\nu(\textd\eta)$. Here $H=\sum_bV(\eta_b)$ is the Hamiltonian, $V$ is a symmetric potential, $\beta>0$ is the inverse temperature, and $\nu$ is the Lebesgue measure on the linear space defined by imposing the loop condition $\eta_{b_1}+\eta_{b_2}=\eta_{b_3}+\eta_{b_4}$ for each plaquette $(b_1,b_2,b_3,b_4)$ in $\Z^2$. For convex $V$, Funaki and Spohn have shown that ergodic infinitevolume Gibbs measures are characterized by their tilt. We describe a mechanism by which the gradient Gibbs measures with nonconvex $V$ undergo a structural, orderdisorder phase transition at some intermediate value of inverse temperature $\beta$. At the transition point, there are at least two distinct gradient measures with zero tilt, i.e., $E \eta_b=0$.
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