We propose a new way of investigating phase transitions in the context of information theory. We use an information-entropic measure of spatial complexity known as configurational entropy (CE) to quantify both the storage and exchange of information in a lattice simulation of a Ginzburg-Landau model with a scalar order parameter coupled to a heat bath. The CE is built from the Fourier spectrum of fluctuations around the mean-field and reaches a minimum at criticality. In particular, we investigate the behavior of CE near and at criticality, exploring the relation between information and the emergence of ordered domains. We show that as the temperature is increased from below, the CE displays three essential scaling regimes at different spatial scales: scale free, turbulent, and critical. Together, they offer an information-entropic characterization of critical behavior where the storage and processing of information is maximized at criticality.
A comparison of results from principal component analysis and support vector machine calculations is made for a variety of phase transitions in two-dimensional classical spin models.
We investigate a phase transition in an SU(3) symmetric spin-1 chain. We identify the universality class of the critical trimer liquid phase, as well as the phase boundary between these two phases.
We investigate the phase transitions of the $q$-state Brownian Potts model in two dimensions (2d) comprising Potts spins that diffuse like Brownian particles and interact ferromagnetically with other spins within a fixed distance. With extensive Monte Carlo simulations we find a continuous phase transition from a paramagnetic to a ferromagnetic phase even for $q>4$. This is in sharp contrast to the existence of a discontinuous phase transition in the equilibrium $q$-state Potts model in 2d with $q>4$. We present detailed numerical evidence for a continuous phase transition and argue that diffu…
Critical transitions, or large changes in the state of a system after a small change in the system's external conditions or parameters, commonly occur in a wide variety of disciplines, from the biological and social sciences to physics. Statistical physics first confronted the problem of emergent phenomena such as critical transitions in the 1800s and 1900s, culminating in the theory of phase transitions. However, although phase transitions show a strong resemblance to critical transitions, the theoretical connections between the two sets of phenomena are tenuous at best, and it would be advan…
We generalize the original majority-vote (MV) model from two states to arbitrary $p$ states and study the order-disorder phase transitions in such a $p$-state MV model on complex networks. By extensive Monte Carlo simulations and a mean-field theory, we show that for $p\geq3$ the order of phase transition is essentially different from a continuous second-order phase transition in the original two-state MV model. Instead, for $p\geq3$ the model displays a discontinuous first-order phase transition, which is manifested by the appearance of the hysteresis phenomenon near the phase transition. Wit…
We consider sudden quenches across quantum phase transitions in the $S=1$ XXZ model starting from the Haldane phase. We demonstrate that dynamical phase transitions may occur during these quenches that are identified by nonanalyticities in the rate function for the return probability. In addition, we show that the temporal behavior of the string order parameter is intimately related to the subsequent dynamical phase transitions. We furthermore find that the dynamical quantum phase transitions can be accompanied by enhanced two-site entanglement.
We review recent advances in understanding the universal scaling properties of non-equilibrium phase transitions in non-ergodic disordered systems. We discuss dynamical critical points (also known as eigenstate phase transitions) between different many-body localized (MBL) phases, and between MBL and thermal phases.
We consider a free fermion formulation of a statistical model exhibiting a limit shape phenomenon. The model is shown to have a phase transition that can be visualized as the merger of two liquid regions - arctic circles. We show that the merging arctic circles provide a space-time resolved picture of the phase transition in lattice QCD known as Gross-Witten-Wadia transition. The latter is a continuous phase transition of the third order. We argue that this transition is universal and is not spoiled by interactions if parity and time-reversal symmetries are preserved. We refer to this universa…
The existence and search for thermodynamic phase transitions is of unfading interest. In this paper, we present numerical evidence of dynamical phase transitions occurring in boundary driven systems with a constrained integrated current. It is shown that certain models exhibit a discontinuous transition between two different density profiles and a continuous transition between a time-independent and a time-dependent profile. We also checked that the KMP model does not exhibit phase transition in a range much larger than previously explored.
We review recent developments in structural-dynamical phase transitions in trajectory space. An open question is how the dynamic facilitation theory of the glass transition may be reconciled with thermodynamic theories that posit a vanishing configurational entropy. Dynamic facilitation theory invokes a dynamical phase transition, between an active phase (close to the normal liquid) and an inactive phase which is glassy, whose order parameter is either dynamic or a time-averaged structural quantity. In particular, the dynamical phase transition in systems with non-trivial thermodynamics manife…
The glass transition is considered as a phase transition in the system of topologically protected excitations in matter structure. The critical behavior of the system is considered both in statics and dynamics cases. It is shown in the simple model describing the topological defects system in the elastic medium with non-zero shear modulus, most of characteristic thermodynamic and kinetic properties of glass transition are reproduced: the Vogel--Fulcher--Tammann law; the behavior of susceptibility, and non-linear susceptibilities; heat capacity behavior; and boson peak near the glass transition…
Dynamical phase transitions are defined as non-analytic points of the large deviation function of current fluctuations. We show that for boundary driven systems, many dynamical phase transitions can be identified using the geometrical structure of an effective potential of a Hamiltonian, recovered from the macroscopic fluctuation theory description. Using this method we identify new dynamical phase transitions that could not be recovered using existing perturbative methods. Moreover, using the Hamiltonian picture, an experimental scheme is suggested to demonstrate an analog of dynamical phase …
In this work we investigate the order of the phase transition of the spin-1 Baxter-Wu model. We used extensive entropic simulations to describe the behavior of quantities which reveal the order of the phase transition. We applyied finite-sizing scaling laws for continuous and discontinuous phase transitions. Our results show that this system exhibits an indeterminacy regarding the order of the phase transition, i.e., the results are conclusive for both transitions, whether continuous or discontinuous. In such a scenario we carried out a study of the configurations in the region of the phase tr…
In this article we provide a review of geometrical methods employed in the analysis of quantum phase transitions and non-equilibrium dissipative phase transitions. After a pedagogical introduction to geometric phases and geometric information in the characterisation of quantum phase transitions, we describe recent developments of geometrical approaches based on mixed-state generalisation of the Berry-phase, i.e. the Uhlmann geometric phase, for the investigation of non-equilibrium steady-state quantum phase transitions (NESS-QPTs ). Equilibrium phase transitions fall invariably into two marked…
A crowd of nonequilibrium entities can show phase transition behaviors that are prohibited in conventional equilibrium setups. An interesting question is whether similar activity-driven phase transitions also occur in pure quantum systems. Here we introduce a minimally simple quantum many-body model that undergoes quantum phase transitions induced by non-Hermiticity. The model is based on a classical anisotropic lattice gas model that undergoes motility-induced phase separation (MIPS), and the quantum phase diagram includes other active phases such as the flocking phase. The quantum phase tran…
We explore quantum phase transitions using two probes of quantum chaos: out-of-time-order correlators (OTOCs) and the $r$-parameter obtained from the level spacing statistics. In particular, we address $p$-spin models associated with quantum annealing or reverse annealing. Quantum annealing triggers first-order or second-order phase transitions, which is crucial for the performance of quantum devices. We find that the time-averaging OTOCs for the ground state and the average $r$-parameter change behavior around the corresponding transition points, diagnosing the phase transition. Furthermore, …
