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The equation of state of a system at equilibrium may be derived from the canonical or the grand canonical partition function. The former is a function of temperature T, while the latter also depends on the chemical potential mu for diffusive equilibrium. In the literature, often the variables beta=(k_BT)^{-1} and fugacity z=exp(beta mu) are used instead. For real beta and z, the partition functions are always positive, being sums of positive terms. Following Lee, Yang and Fisher, we point out that valuable information about the system may be gleaned by examining the zeros of the grand partition function in the complex z plane (real beta), or of the canonical partition function in the complex beta plane. In case there is a phase transition, these zeros close in on the real axis in the thermodynamic limit. Examples are given from the van der Waal gas, and from the ideal Bose gas, where we show that even for a finite system with a small number of particles, the method is useful.
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We calculate zeros of the $q$-state Potts model partition function on $m$th-iterate Sierpinski graphs, $S_m$, in the variable $q$ and in a temperature-like variable, $y$. We infer some asymptotic properties of the loci of zeros in the limit $m to infty$ and relate these to thermodynamic properties of the $q$-state Potts ferromagnet and antiferromagnet on the Sierpinski gasket fractal, $S_infty$.
We introduce the Loschmidt amplitude as a powerful tool to perform spectroscopy of generic many-body wave functions and use it to interrogate the wave function obtained after ramping the transverse field quantum Ising model through its quantum critical point. Previous results are confirmed and a more complete understanding of the population of defects and of the effects of magnon-magnon interaction or finite-size corrections is obtained. The influence of quantum coherence is clarified.
Dark states are stationary states of a dissipative, Lindblad-type time evolution with zero von Neumann entropy, therefore representing examples of pure, steady quantum states. Non-equilibrium dynamics featuring a dark state recently gained a lot of attraction since their implementation in the context of driven-open quantum systems represents a viable possibility to engineer unique, pure states. In this work, we analyze a driven many-body spin system, which undergoes a transition from a dark steady state to a mixed steady state as a function of the driving strength. This transition connects a zero entropy (dark) state with a finite entropy (mixed) state and thus goes beyond the realm of equilibrium statistical mechanics and becomes of genuine nonequilibrium character. We analyze the relevant long wavelength fluctuations driving this transition in a regime where the system performs a discontinuous jump from a dark to a mixed state by means of the renormalization group. This allows us to approach the nonequilibrium dark state transition and identify similarities and clear differences to common, equilibrium phase transitions, and to establish the phenomenology for a first order dark state phase transition.
We discuss the origin of topological defects in phase transitions and analyze their role as a diagnostic tool in the study of the non-equilibrium dynamics of symmetry breaking. Homogeneous second order phase transitions are the focus of our attention, but the same paradigm is applied to the cross-over and inhomogeneous transitions. The discrepancy between the experimental results in 3He and 4He is discussed in the light of recent numerical studies. The possible role of the Ginzburg regime in determining the vortex line density for the case of a quench in 4He is raised and tentatively dismissed. The difference in the anticipated origin of the dominant signal in the two (3He and 4He) cases is pointed out and the resulting consequences for the subsequent decay of vorticity are noted. The possibility of a significant discrepancy between the effective field theory and (quantum) kinetic theory descriptions of the order parameter is briefly touched upon, using atomic Bose-Einstein condensates as an example.
The physics of highly excited Rydberg atoms is governed by blockade or exclusion interactions that hinder the excitation of atoms in the proximity of a previously excited one. This leads to cooperative effects and a relaxation dynamics displaying space-time heterogeneity similar to what is observed in the relaxation of glass-forming systems. Here we establish theoretically the existence of a glassy dynamical regime in an open Rydberg gas, associated with phase coexistence at a first-order transition in dynamical large deviation functions. This transition occurs between an active phase of low density in which dynamical processes take place on short timescales, and an inactive phase in which excited atoms are dense and the dynamics is highly arrested. We perform a numerically exact study and develop a mean-field approach that allows to understand the mechanics of this phase transition. We show that radiative decay --- which becomes experimentally relevant for long times --- moves the system away from dynamical phase coexistence. Nevertheless, the dynamical phase transition persists and causes strong fluctuations in the observed dynamics.
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