First-Order Spin Glass Transitions: an Exact Solution

Mottishaw, Peter

doi:10.1209/0295-5075/1/8/007

Cited by 31 publications

(37 citation statements)

References 12 publications

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“…Theoretically such behavior occurs in spin glasses in a transverse field, see e.g. [26] [27] [28] [29].…”

Section: Thermodynamic Picture For a System Described By An Effecmentioning

confidence: 99%

Thermodynamic picture of the glassy state gained from exactly solvable models

Nieuwenhuizen

2000

Phys. Rev. E

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A picture for thermodynamics of the glassy state was introduced recently by us [Phys. Rev. Lett. 79, 1317 (1997); 80, 5580 (1998)]. It starts by assuming that one extra parameter, the effective temperature, is needed to describe the glassy state. This approach connects responses of macroscopic observables to a field change with their temporal fluctuations, and with the fluctuation-dissipation relation, in a generalized, nonequilibrium way. Similar universal relations do not hold between energy fluctuations and the specific heat. In the present paper, the underlying arguments are discussed in greater length. The main part of the paper involves details of the exact dynamical solution of two simple models introduced recently: uncoupled harmonic oscillators subject to parallel Monte Carlo dynamics, and independent spherical spins in a random field with such dynamics. At low temperature, the relaxation time of both models diverges as an Arrhenius law, which causes glassy behavior in typical situations. In the glassy regime, we are able to verify the above-mentioned relations for the thermodynamics of the glassy state. In the course of the analysis, it is argued that stretched exponential behavior is not a fundamental property of the glassy state, though it may be useful for fitting in a limited parameter regime.

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“…Theoretically such behavior occurs in spin glasses in a transverse field, see e.g. [26] [27] [28] [29].…”

Section: Thermodynamic Picture For a System Described By An Effecmentioning

confidence: 99%

Thermodynamic picture of the glassy state gained from exactly solvable models

Nieuwenhuizen

2000

Phys. Rev. E

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“…If instead one wishes to model a structural (fragile) glass behavior, one may choose interactions as in either the random orthogonal model [17], or to consider a p-spin interaction model with spin-1 variables like in Ref. [18]. We have studied the equilibrium phase diagram of the former model in detail and found, for large enough r, a reentrant behaviour in both the dynamic and static glass transition line.…”

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confidence: 99%

Shear-Thickening and Entropy-Driven Reentrance

Sellitto

Kurchan²

2005

Phys. Rev. Lett.

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We discuss a generic mechanism for shear-thickening analogous to entropy-driven phase reentrance. We implement it in the context of non-relaxational mean-field glassy systems: although very simple, the microscopic models we study present a dynamical phase diagram with second and first order stirring-induced jamming transitions leading to intermittency, metastability and phase coexistence as seen in some experiments. The jammed state is fragile with respect to change in the stirring direction. Our approach provides a direct derivation of a Mode-Coupling theory of shear-thickening.When liquids are subjected to strong stirring, in general their viscosity decreases, a phenomenon known as 'shear thinning'. The opposite ('shear thickening') behavior when stirring leads to increased jamming is rather exceptional and intriguing [1]. That shear-thinning should be generic is quite easy to understand by considering the structure of any system having a large viscosity and long relaxation time scales. From the point of view of the phase-space energy landscape, the long relaxation times are the consequence of directions that are either almost flat, or contain barriers that can only just be crossed. When the system is stirred by non-conservative forces, displacements are easily induced along these directions, and this has the effect of speeding the relaxation. From the real space point of view, slow relaxations are linked to extended dynamically correlated spatial regions [2], and stirring tends to break off these domains, thus making the system more fluid. It is thus no surprise that just about any system (and any model) will naturally exhibit shear-thinning.For shear-thickening instead, several explanations have been attempted, and it is at present not clear whether a universal one will apply for all possible systems. There are indications that jamming in particulate suspensions is related to increased disorder [3], and in some cases to the formation of clusters of particles in lubrication contact [4,5]. To the extent that at large densities the strongly jammed state has the appearance of an amorphous, glassy solid, shear-thickening may be thought of as a consequence of an underlying glass transition induced by stirring [6]. For such collective behavior one can attempt a theory with less focus on the details but founded on notions that are thought to be generic of glasses: this has suggested, for example, the casting of the problem in a Mode Coupling format [6].In this Letter we attempt a microscopic setting in which glassiness and shear-thickening emerge naturally and are simultaneously understood. The basic idea is to exploit the analogy between entropy-driven transitions in which systems freeze upon heating and those in which they jam under the action of stirring. To obtain concrete results, we discuss this idea within the 'Random First Order' scenario for the glass transition, although it is not restricted to it. In its simplest version, the Random First Order scenario applies to models of fully connected degrees of free...

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“…Several models for magnets undergoing a first order glassy transitions with a latent heat have been studied in the literature [14] …”

Section: Modified Clausius-clapeyron Relationmentioning

confidence: 99%

“…The result for a glass forming liquid may be written as ∆α = ∆κ dp g dT (14) while for a glassy magnet…”

Section: Ehrenfest Relations and Prigogine-defay Ratiomentioning

confidence: 99%

Thermodynamics of the Glassy State

Leuzzi¹,

Nieuwenhuizen

2007

113

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Abstract.A picture for thermodynamics of the glassy state is introduced. It assumes that one extra parameter, the effective temperature, is needed to describe the glassy state. This explains the classical paradoxes concerning the Ehrenfest relations and the PrigogineDefay ratio.As a second part, the approach connects the response of macroscopic observables to a field change with their temporal fluctuations, and with the fluctuation-dissipation relation, in a generalized non-equilibrium way. I INTRODUCTIONNon-equilibrium thermodynamics for systems far from equilibrium has long been a field of confusion. A typical application is window glass. Such a system is far from equilibrium: a cubic micron of glass is neither a crystal nor an ordinary undercooled liquid. It is an under-cooled liquid that, in the glass formation process, has fallen out of its meta-stable equilibrium.Until our recent works on this field, the general consensus reached after more than half a century of research was: Thermodynamics does not work for glasses, because there is no equilibrium [1]. This conclusion was mainly based on the failure to understand the Ehrenfest relations and the related Prigogine-Defay ratio. It should be kept in mind that, so far, the approaches leaned very much on equilibrium ideas. Well known examples are the 1951 Davies-Jones paper [2], the 1958 GibbsDiMarzio [3] and the 1965 Adam-Gibbs [4] papers, while a 1981 paper by DiMarzio has title "Equilibrium theory of glasses" and a subtitle "An equilibrium theory of glasses is absolutely necessary" [5]. We shall stress that such approaches are not applicable, due to the inherent non-equilibrium character of the glassy state.Thermodynamics is the most robust field of physics. Its failure to describe the glassy state is quite unsatisfactory, since up to 25 decades in time can be involved. Naively we expect that each decade has its own dynamics, basically independent of the other ones. We have found support for this point in models that can be solved exactly. Thermodynamics then means a description of system properties under smooth enough non-equilibrium conditions.

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First-Order Spin Glass Transitions: an Exact Solution

Cited by 31 publications

References 12 publications

Thermodynamic picture of the glassy state gained from exactly solvable models

Thermodynamic picture of the glassy state gained from exactly solvable models

Shear-Thickening and Entropy-Driven Reentrance

Thermodynamics of the Glassy State

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