Spin-glass transition in a magnetic field: A renormalization group study

Pimentel, I. R.; Temesvári, T.; Dominicis, C. De

doi:10.1103/physrevb.65.224420

Cited by 48 publications

(81 citation statements)

References 26 publications

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“…As expected, the results of the fixed points of the renormalization group equations are the same if the non critical modes are also taken into account [42]. The action that one obtains reads: [41,42] …”

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confidence: 72%

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Gardner transition in finite dimensions

Urbani

Biroli

2015

Phys. Rev. B

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Recent works on hard spheres in the limit of infinite dimensions revealed that glass states, envisioned as meta-basins in configuration space, can break up in a multitude of separate basins at low enough temperature or high enough pressure, leading to the emergence of new kinds of soft-modes and unusual properties. In this paper we study by perturbative renormalisation group techniques the critical properties of this transition, which has been discovered in disordered mean-field models in the '80s. We find that the upper critical dimension du above which mean-field results hold is strictly larger than six and apparently non-universal, i.e. system dependent. Below du, we do not find any perturbative attractive fixed point (except for a tiny region of the 1RSB breaking parameter), thus showing that the transition in three dimensions either is governed by a non-perturbative fixed point unrelated to the Gaussian mean-field one or becomes first order or does not exist. We also discuss possible relationships with the behavior of spin glasses in a field.The properties of glasses at low temperatures are the subject of extensive experimental, numerical and analytical investigations. In order to understand them, one has to study the properties of the amorphous solids in which liquids freeze at the glass transition. Hence a crucial preliminary step is arguably understanding glassformation. One of the most prominent theoretical approaches to do that is the Random First Order Transition (RFOT) theory introduced by Kirkpatrick, Thirumalai, and Wolynes [1][2][3][4]. It has its roots in the mean-field theory of disordered models but, as it has become clear in recent years, it goes well beyond that. RFOT theory applies to all systems characterized by a certain kind of (free-)energy landscape, such that below a given temperature T d an exponential number (in the system size) of metastable states emerges. By lowering the temperature their thermodynamics becomes ruled by the competition between two kinds of contributions: one (free-energetic) that favours states with lower internal free energy because their corresponding Boltzmann weight is larger, and the other (entropic) which favours states having high internal free energy because they are more numerous. At the so called Kauzmann temperature, T K , the entropic contribution vanishes and the system freezes in one lowlying glass state. RFOT theory advocates that this is precisely what happens for super-cooled liquids approaching the glass transition, where T d corresponds to the so-called Mode Coupling cross-over and T K to the ideal glass transition. A major result of the last thirty years was to show that this is indeed the case within mean-field theory [5]. Actually, the range of systems displaying such an energy landscape-at the mean field level-is remarkably broad: it encompasses physical systems such as super-cooled liquids, colloids, proteins [6,7] and models central in other fields like random K-satisfiability [8]. Whether this remains true beyond the mean-field approximat...

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confidence: 72%

“…This is a standard procedure and it has been already followed in the case of the Edwards-Anderson (EA) model in a field [41]. As expected, the results of the fixed points of the renormalization group equations are the same if the non critical modes are also taken into account [42]. The action that one obtains reads: [41,42] …”

mentioning

confidence: 87%

Gardner transition in finite dimensions

Urbani

Biroli

2015

Phys. Rev. B

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“…[9,15,17,19] -which are needed for the following discussion. Due to the severe technical difficulties, only one-loop calculations have been accomplished (ǫ ≡ 6 − d and n = 0).…”

Section: Formulation Of the Spin Glass Problem Formentioning

confidence: 99%

“…[17]. Using these equations, a new set of parameters g i -the so called nonlinear scaling fields introduced by Wegner [22] -can be defined with the following properties: 8…”

Section: Below Six Dimensionsmentioning

confidence: 99%

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Replica symmetry breaking in and around six dimensions

Parisi¹,

Temesvári²

2012

Nuclear Physics B

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Two, replica symmetry breaking specific, quantities of the Ising spin glass -the breakpoint x 1 of the order parameter function and the Almeida-Thouless line -are calculated in six dimensions (the upper critical dimension of the replicated field theory used), and also below and above it. The results comfirm that replica symmetry breaking does exist below d = 6, and also the tendency of its escalation for decreasing dimension continues. As a new feature, x 1 has a nonzero and universal value for d < 6 at criticality. Near six dimensions. A method to expand a generic theory with replica equivalence around the replica symmetric one is also demonstrated.

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