First-order transitions and triple point on a random p-spin interaction model

The critical behavior of a family of fully connected mean-field models with quenched disorder, the $M-p$ Ising spin glass, is analyzed, displaying a crossover between a continuous and a random first order phase transition as a control parameter is tuned. Due to its microscopic properties the model is straightforwardly extendable to finite dimensions in any geometry.

We study the non-equilibrium phase diagram of a fully-connected Ising $p$-spin model, for generic $p>2$, and investigate its robustness with respect to the inclusion of spin-wave fluctuations, resulting from a ferromagnetic, short-range spin interaction. In particular, we investigate the dynamics of the mean-field model after a quantum quench: we observe a new dynamical phase transition which is either first or second order depending on the even or odd parity of $p$, in stark...

We introduce and study a model which admits a complex landscape without containing quenched disorder. Continuing our previous investigation we introduce a disordered model which allows us to reconstruct all the main features of the original phase diagram, including a low $T$ spin glass phase and a complex dynamical behavior.

The effects of random magnetic fields are considered in an Ising spin-glass model defined in the limit of infinite-range interactions. The probability distribution for the random magnetic fields is a double Gaussian, which consists of two Gaussian distributions centered respectively, at $+H_{0}$ and $-H_{0}$, presenting the same width $\sigma$. It is argued that such a distribution is more appropriate for a theoretical description of real systems than its simpler particular t...

We study a $p$-spin model with ferromagnetic coupling and quenched random-crystal fields for $p \ge 3$ for spin-1 systems. We find that the model has lines of first order transitions at finite temperature $(T)$ for all $p \ge 3$. For bimodal distribution of the random-crystal field these lines meet at a \emph{triple point} for weak strength of the crystal field $(\Delta)$. Beyond a critical strength of $\Delta$, they do not meet and one of the lines ends at a \emph{critical p...

The infinite-range-interaction Ising spin glass is considered in the presence of an external random magnetic field following a trimodal (three-peak) distribution. The model is studied through the replica method and phase diagrams are obtained within the replica-symmetry approximation. It is shown that the border of the ferromagnetic phase may present first-order phase transitions, as well as tricritical points at finite temperatures. Analogous to what happens for the Ising fe...

The dynamic phase transitions have been studied, within a mean-field approach, in the kinetic spin-1 Ising model Hamiltonian with arbitrary bilinear and biquadratic pair interactions in the presence of a time varying (sinusoidal) magnetic field by using the Glauber-type stochastic dynamics. The nature (first- or second-order) of the transition is characterized by investigating the behavior of the thermal variation of the dynamic order parameters. The dynamic phase transitions...

We consider the thermodynamics of an infinite-range Ising p-spin glass model with an additional r-spin ferromagnetic interaction. For r=2 there is a continuous transition to a ferromagnetic phase, while for r>2 the transition is first order. We find both glassy and non-glassy ferromagnetic phases, with replica symmetry breaking of both the one step and full varieties. We obtain new results for the case where r=p>2, demonstrating the existence of a non-glassy ferromagnetic pha...

We examine the phase diagram of the $p$-spin mean field glass model in the spin one case, that is when $S=0,+1,-1$. For large $p$ the model is solved exactly. The analysis reveals that the phase diagram is in some way similar to that of Ising spins. However, as we show, the quadrupolar regular ordering as well as qudrupolar glass order are present now. The temperature of the Gardner 1RSB -- FRSB transition is obtained explicitly for large $p$. The case of higher spins is disc...

In this talk I will review the approach to spin glasses based on the spontaneously broken replica symmetry. I will concentrate my attention mostly on more general ideas, skipping technical details and stressing the characteristic predictions of this approach. After the introduction of the replica method, the predicted structure of states is investigated in details, paying a particular attention to the local overlaps and to the structure of the clusters. I will finally study t...