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We analyze Mode Coupling discontinuous transition in the limit of vanishing discontinuity, approaching the so called $A_3$ point. In these conditions structural relaxation and fluctuations appear to have universal form independent from the details of the system. The analysis of this limiting case suggests new ways for looking at the Mode Coupling equations in the general case.
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Discontinuous phase transitions out of equilibrium can be characterized by the behavior of macroscopic stochastic currents. But while much is known about the the average current, the situation is much less understood for higher statistics. In this paper, we address the consequences of the diverging metastability lifetime -- a hallmark of discontinuous transitions -- in the fluctuations of arbitrary thermodynamic currents, including the entropy production. In particular, we center our discussion on the emph{conditional} statistics, given which phase the system is in. We highlight the interplay between integration window and metastability lifetime, which is not manifested in the average current, but strongly influences the fluctuations. We introduce conditional currents and find, among other predictions, their connection to average and scaled variance through a finite-time version of Large Deviation Theory and a minimal model. Our results are then further verified in two paradigmatic models of discontinuous transitions: Schlogls model of chemical reactions, and a $12$-states Potts model subject to two baths at different temperatures.
We study the time-averaged flow in a model of particles that randomly hop on a finite directed graph. In the limit as the number of particles and the time window go to infinity but the graph remains finite, the large-deviation rate functional of the average flow is given by a variational formulation involving paths of the density and flow. We give sufficient conditions under which the large deviations of a given time averaged flow is determined by paths that are constant in time. We then consider a class of models on a discrete ring for which it is possible to show that a better strategy is obtained producing a time-dependent path. This phenomenon, called a dynamical phase transition, is known to occur for some particle systems in the hydrodynamic scaling limit, which is thus extended to the setting of a finite graph.
The effects of quenched disorder on nonequilibrium phase transitions in the directed percolation universality class are revisited. Using a strong-disorder energy-space renormalization group, it is shown that for any amount of disorder the critical behavior is controlled by an infinite-randomness fixed point in the universality class of the random transverse-field Ising models. The experimental relevance of our results are discussed.
We investigate the generalized p-spin models that contain arbitrary diagonal operators U with no reflection symmetry. We derive general equations that give an opportunity to uncover the behavior of the system near the glass transition at different (continuous) p. The quadrupole glass with J=1 is considered as an illustrating example. It is shown that the crossover from continuous to discontinuous glass transition to one-step replica breaking solution takes place at p=3.3 for this model. For p <2+Delta p, where Delta p= 0.5 is a finite value, stable 1RSB-solution disappears. This behaviour is strongly different from that of the p-spin Ising glass model.
We study the dynamics arising from a double quantum quench where the parameters of a given Hamiltonian are abruptly changed from being in an equilibrium phase A to a different phase B and back (A$to$B$to$A). As prototype models, we consider the (integrable) transverse field Ising as well as the (non-integrable) ANNNI model. The return amplitude features non-analyticities after the first quench through the equilibrium quantum critical point (A$to$B), which is routinely taken as a signature of passing through a so-called dynamical quantum phase transition. We demonstrate that non-analyticities after the second quench (B$to$A) can be avoided and reestablished in a recurring manner upon increasing the time $T$ spent in phase B. The system retains an infinite memory of its past state, and one has the intriguing opportunity to control at will whether or not dynamical quantum phase transitions appear after the second quench.
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