Universal scaling effects of a temperature gradient at first-order transitions

Theory of pinned fronts

The properties of a front between two different phases in the presence of a smoothly inhomogeneous external field that takes its critical value at the crossing point is analyzed. Two generic scenarios are studied. In the first, the system admits a bistable solution and the external field governs the rate in which one phase invades the other. The second mechanism corresponds to a continuous transition that, in the case of reactive systems, takes the form of a transcritical bifurcation at the crossing point. We solve for the front shape and for the response of competitive fronts to external noise, showing that static properties and also some of the dynamical features cannot discriminate between the two scenarios. A reliable indicator turns out to be the fluctuation statistics. These take a Gaussian form in the bifurcation case and a double-peaked shape in a bistable system. Our results are discussed in the context of biological processes, such as species and communities dynamics in the presence of a resource gradient.

Off-equilibrium scaling behaviors across first-order transitions

We study off-equilibrium behaviors at first-order transitions (FOTs) driven by a time dependence of the temperature across the transition point T(c), such as the linear behavior T(t)/T(c)=1±t/t(s) where t(s) is a time scale. In particular, we investigate the possibility of nontrivial off-equilibrium scaling behaviors in the regime of slow changes, corresponding to large t(s). We consider the two-dimensional Potts models, which provide an ideal theoretical laboratory to investigate issues related to FOTs driven by thermal fluctuations. We put forward general ansatzes for off-equilibrium scaling behaviors around the time t=0 corresponding to T(c). Then we present numerical results for the q=10 and 20 Potts models. We show that off-equilibrium scaling behaviors emerge at FOTs with relaxational dynamics, when appropriate boundary conditions are considered, such as mixed boundary conditions favoring different phases at the opposite sides of the system, which enforce an interface in the system.

Finite-size scaling at the first-order quantum transitions of quantum Potts chains

We investigate finite-size effects at first-order quantum transitions. For this purpose we consider the one-dimensional q-state quantum Potts chain, in particular with q=10, which undergoes a first-order transition, separating the quantum disordered and ordered phases with a discontinuity in the energy density of the ground state. In agreement with the general theory, around the transition the low-energy properties show finite-size scaling with respect to appropriate scaling variables. Their size dependence is particularly sensitive to boundary conditions, which is a specific feature of first-order quantum transitions. Finally, we also discuss the finite-size behavior of the q-state Potts model (q≥2) at the first-order transitions driven by a parallel magnetic field, occurring in the ferromagnetic phase.

Scaling phenomena driven by inhomogeneous conditions at first-order quantum transitions

We investigate the effects of smooth inhomogeneities at first-order quantum transitions (FOQTs), such as those arising in the presence of a space-dependent external field, which smooths out the discontinuities of the low-energy properties at the transition. We argue that a universal scaling behavior emerges in the space transition region close to the point in which the external field takes the value for which the homogeneous system undergoes the FOQT. We verify the general theory in two model systems. We consider the quantum Ising chain in the ferromagnetic phase and the q-state Potts chain for q=10, investigating the scaling behavior which arises in the presence of an additional inhomogeneous parallel and transverse magnetic field, respectively. Numerical results are in full agreement with the general theory.