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Abstract We present Monte Carlo simulations of the two-dimensional one-component plasma (2D OCP) confined to a cylindrical geometry, focusing on density profiles, fluctuations, and their connection to bulk correlation functions. The cylindrical geometry eliminates geometric frustration, allowing for a precise study of boundary density oscillations, the dependence on boundary conditions, and their relationship to the melting transition and triangular lattice structure. By triangulating particle configurations, we quantify the exponential suppression of topological defects in the crystalline phase. Furthermore, we propose an oriented correlation function that better links boundary density profiles with bulk correlation functions, motivating anisotropic generalizations of the phase-field crystal model. These results provide new insights into the interplay between boundary effects, bulk correlations, and phase transitions in the 2D OCP. 

The emptiness formation problem is addressed for a one-dimensional quantum polytropic gas characterized by an arbitrary polytropic index $$\gamma$$, which defines the equation of state $$P \sim \rho^\gamma$$, where $$P$$ is the pressure and $$\rho$$ is the density. The problem involves determining the probability of the spontaneous formation of an empty interval in the ground state of the gas. In the limit of a macroscopically large interval, this probability is dominated by an instanton configuration. By solving the hydrodynamic equations in imaginary time, we derive the analytic form of the emptiness instanton. This solution is expressed as an integral representation analogous to those used for correlation functions in Conformal Field Theory. Prominent features of the spatiotemporal profile of the instanton are obtained directly from this representation. 

We consider directed polymers in $1+1$spatial dimension under action of an external repulsive potential along a line. Using the exact mapping onto imaginary time evolution of free fermions we find that for sufficiently strong potential the system of polymers undergoes a continuous configurational phase transition. The transition corresponds to merging empty regions in the dominant limit shape. 

A<sc>bstract</sc> Euler hydrodynamics of perfect fluids can be viewed as an effective bosonic field theory. In cases when the underlying microscopic system involves Dirac fermions, the quantum anomalies should be properly described. In 1+1 dimensions the action formulation of hydrodynamics at zero temperature is reconsidered and shown to be equal to standard field-theory bosonization. Furthermore, it can be derived from a topological gauge theory in one extra dimension, which identifies the fluid variables through the anomaly inflow relations. Extending this framework to 3+1 dimensions yields an effective field theory/hydrodynamics model, capable of elucidating the mixed axial-vector and axial-gravitational anomalies of Dirac fermions. This formulation provides a platform for bosonization in higher dimensions. Moreover, the connection with 4+1 dimensional topological theories suggests some generalizations of fluid dynamics involving additional degrees of freedom. 

Abstract 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 universal transition as the merger transition.