How to compute the thermodynamics of a glass using a cloned liquid

Abstract

The recently proposed strategy for studying the equilibrium thermodynamics of the glass phase using a molecular liquid is reviewed and tested in details on the solvable case of the $p$-spin model. We derive the general phase diagram, and confirm the validity of this procedure. We point out the efficacy of a system of two weakly coupled copies in order to identify the glass transition, and the necessity to study a system with $m<1$ copies ('clones') of the original problem in order to derive the thermodynamic properties of the glass phase.Comment: Latex, 17 pages, 6 figure

Monte Carlo study of the metamagnet Ising model in a random and uniform field

“…In the last ten years, the physics of the hysteresis, of the avalanche behavior and of the origin of self-organized criticality [20] have been modelled employing the non-equilibrium behavior of the RFIM. In particular, a new class of problems, such as self-generated glassy behavior, has been studied through the non-disordered model with infinitesimal random field [21]. Recently, random magnetic fields have been considered in metamagnet systems of Ising type.…”

Replica-symmetry breaking in long-range glass models without quenched disorder

“…Very recently the cloning method was proposed that is based on the idea that even at low T a system of m clones might be distributed in its phase space over many low lying metastable states if m is chosen correctly and the properties of all these states are essentially equivalent to those of the ground state. [3][4][5][6] Generally, the partition sum of m weakly coupled clones is F e −N (mβF −S conf (F )) , where sum goes over free energies (per site) of metastable states, F , and S conf (F ) is their configurational entropy (S conf = 1 N ln(N states )). Assuming that dS conf (F )/dF is finite at the lowest F associated with the ground state one needs to chose m ∝ T at low T in order to avoid a complete dominance by a single (ground) state and the problems with site nonequivalence mentioned above.…”

“…Averaging over the random field configurations is performed in the usual way introducing n replicas of the system and taking the limit n → 0. The assumption of uncorrelated states is equivalent to one step replica symmetry breaking (1RSB) formalism; further, in this case this method is formally equivalent to cloned liquid approach if the size of the blocks in 1RSB is equal to the number of clones (see [6] for the discussion of replica method vs clones for quenched disordered glasses). From the above discussion it is evident that another assumption implicit in this approach is that the energy spacing between low lying states should be much less than O( √ N ) if it is too big a small magnetic field will not be sufficient to rearrange low lying states, if it is too small, e.g.…”

“…Now we turn to the model (6). Here the self energy is diagonal in the site index by construction, further, the interaction part of this model is the same as for model (5)…”

“…The value m = 1 defines the "dynamical" critical temperature T g ≈ 0.13363. The free energy functional (4) corresponding to 1RSB ansatz is equivalent to the free energy functional that is obtained in the cloned liquid approach with m being equal to the number of the clones [6]. The stability of the 1RSB solution indicates that the main assumptions of this approach are correct in some temperature range below T g and, therefore, in this temperature range the configurational entropy is given by S conf = m 2 ∂F ∂m .…”