We study the spectrum of the Hessian of the Sherrington-Kirkpatrick model near T = 0, whose eigenvalues are the masses of the bare propagators in the expansion around the mean-field solution. In the limit T << 1 two regions can be identified. The first for x close to 0, where x is the Parisi replica-symmetry-breaking scheme parameter. In this region the spectrum of the Hessian is not trivial, and maintains the structure of the full replica-symmetry-breaking state found at higher temperatures. In the second region T << x <= 1 as T -> 0, the bands typical of the full replica-symmetry-breaking state collapse and only two eigenvalues are found: a null one and a positive one. We argue that this region has a droplet-like behavior. In the limit T -> 0 the width of the full replica-symmetry-breaking region shrinks to zero and only the droplet-like scenario survives. Copyright (C) EPLA, 2010
Low-temperature mass spectrum in the Ising spin glass / Crisanti, Andrea; C., De Dominicis. - In: EUROPHYSICS LETTERS. - ISSN 0295-5075. - STAMPA. - 92:1(2010), pp. 17003-17003-p5. [10.1209/0295-5075/92/17003]
Low-temperature mass spectrum in the Ising spin glass
CRISANTI, Andrea;
2010
Abstract
We study the spectrum of the Hessian of the Sherrington-Kirkpatrick model near T = 0, whose eigenvalues are the masses of the bare propagators in the expansion around the mean-field solution. In the limit T << 1 two regions can be identified. The first for x close to 0, where x is the Parisi replica-symmetry-breaking scheme parameter. In this region the spectrum of the Hessian is not trivial, and maintains the structure of the full replica-symmetry-breaking state found at higher temperatures. In the second region T << x <= 1 as T -> 0, the bands typical of the full replica-symmetry-breaking state collapse and only two eigenvalues are found: a null one and a positive one. We argue that this region has a droplet-like behavior. In the limit T -> 0 the width of the full replica-symmetry-breaking region shrinks to zero and only the droplet-like scenario survives. Copyright (C) EPLA, 2010I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.