Role of the transverse field in inverse freezing in the fermionic Ising spin-glass model

Abstract

We investigate the inverse freezing in the fermionic Ising spin-glass (FISG) model in a transverse field Γ. The grand canonical potential is calculated in the static approximation, replica symmetry and one-step replica symmetry breaking Parisi scheme. It is argued that the average occupation per site n is strongly affected by Γ. As consequence, the boundary phase is modified and, therefore, the reentrance associated with the inverse freezing is modified too. PACS numbers:The inverse transitions (melting or freezing), first proposed by Tammann 1 , are a class of a quite interesting phase transitions, utterly counterintuitive, in which the ordered phase has more entropy than the disordered one 2 . Despite this apparent unconventional thermodynamics, there is now a list plenty of physical systems in which this sort of transition appears (see Ref. 2 and references therein) including, interestingly, high temperature superconductors. 3 In that sense, the search for theoretical models which contain the necessary ingredients to produce such transitions has become a challenging issue as can be seen in Refs. 2 and 4,5,6. However, much less considerations have been given to models in which quantum effects can also be taken into account.

Static critical exponents of the ferromagnetic transition in spin glass re-entrant systems

“…Examples are spin-wave excitations [12], magnetic relaxation [13] and critical properties near T c [14][15][16][17]. The re-entrant magnetic behavior is now being related to the inverse freezing problem [18] which is a current theoretical challenge aimed to describe unconventional transitions where the low temperature phase looks more entropic than the state at higher temperatures [19].…”

Inverse freezing in the Hopfield fermionic Ising spin glass

“…1 and 2 have found that, in such first-order boundary phase, the reentrance and, therefore, the inverse freezing are not essentially affected by the use of RS or 1S-RSB schemes similar to the FISG model. 7 In Fig. 1, it is presented phase diagrams which illustrate two quite distinct situations concerning the degree of frustration.…”

“…It should be remarked that this phase diagram is quite similar to that one found for the FISG model. 7 The location of the boundaries phases in Fig. 1 has been checked in the limits = 0 and T = 0 as it can be seen in Appendices B and C.…”

“…It has been found in previous works 2,5,7 that the use of the RSB schemes in GS or FISG models essentially preserves the reentrance in the SG/PM first-order boundary phase associated to the inverse freezing. There are only small differences which appear mainly at very low temperatures.…”

Inverse transitions in a spin-glass model on a scale-free network

“…For this purpose, we consider the Ghatak-Sherrington (GS) model [15,16], a spin-1 SG model with a crystal field. Recently, the GS model has become well known as a prototypical model for inverse transition [17][18][19][20][21].…”