Related papers: Locating Critical Points Using Ratios of Lee-Yang …
We consider binary liquid mixtures near their critical consolute points and exposed to geometrically flat but chemically structured substrates. The chemical contrast between the various substrate structures amounts to opposite local…
Due to the finite size effects, the localisation of the phase transition in finite systems and the determination of its order, become an extremely difficult task, even in the simplest known cases. In order to identify and locate the finite…
A criterion to locate tricritical points in phase diagrams is proposed. The criterion is formulated in the framework of the Elementary Catastrophe Theory and encompasses all the existing criteria in that it applies to systems described by a…
This paper addresses the numerical computation of critical angles between two convex cones in finite-dimensional Euclidean spaces. We present a novel approach to computing these critical angles by reducing the problem to finding stationary…
We use high-order cumulants to investigate the Lee-Yang zeros of generating functions of dynamical observables in open quantum systems. At long times the generating functions take on a large deviation form with singularities of the…
In this paper we apply the global isomorphism approach [V.~L. Kulinskii, J. Phys. Chem. B \textbf{114} 2852 (2010)] between the Lennard-Jones fluids and Lattice Gas model to the study of the liquid-vapor equilibrium for the systems with the…
Piecewise-linear (PL) Morse theory and discrete Morse theory are used in shape analysis tasks to investigate the topological features of discretized spaces. In spite of their common origin in smooth Morse theory, various notions of critical…
We study the asymptotics of correlations and nearest neighbor spacings between zeros and holomorphic critical points of $p_N$, a degree N Hermitian Gaussian random polynomial in the sense of Shiffman and Zeldtich, as N goes to infinity. By…
Central configurations play an important role in the dynamics of the $n$-body problem: they occur as relative equilibria and as asymptotic configurations in colliding trajectories. We illustrate how they can be found as projective fixed…
We study slow variation (both spatial as well as temporal) of a parameter of a system in the vicinity of discontinuous quantum phase transitions, in particular, a discontinuity critical point (DCP) (or a first-order critical point). We…
We review studies of entanglement entropy in systems with quenched randomness, concentrating on universal behavior at strongly random quantum critical points. The disorder-averaged entanglement entropy provides insight into the quantum…
Significant uncertainty of our present knowledge for uranium critical point parameters is under consideration. Present paper is devoted to comparative analysis of possible resolutions for the problem of uranium critical point location, as…
In principle, the probability of configurations, determined by the system's partition function or wave function, encapsulates essential information about phases and phase transitions. Despite the exponentially large configuration space, we…
One or more small holes provide non-destructive windows to observe corresponding closed systems, for example by measuring long time escape rates of particles as a function of hole sizes and positions. To leading order the escape rate of…
Relative equilibria of Lagrangian and Hamiltonian systems with symmetry are critical points of appropriate scalar functions parametrized by the Lie algebra (or its dual) of the symmetry group. Setting aside the structures - symplectic,…
Universality is a fundamental concept in modern physics. For the $q$-state Potts model, the critical exponents are merely determined by the order-parameter symmetry $S_q$, spatial dimensionality and interaction range, independent of…
We present a new unified theory of critical finite-size scaling for lattice statistical mechanical models with periodic boundary conditions above the upper critical dimension. Our theory is based on recent mathematically rigorous results…
We analyze the trajectory of the Lee-Yang edge singularities of the QCD equation of state in the complex baryon chemical potential ($\mu_B$) plane for different values of the temperature by using the recent lattice results for the Taylor…
Numerically locating the critical points of non-convex surfaces is a long-standing problem central to many fields. Recently, the loss surfaces of deep neural networks have been explored to gain insight into outstanding questions in…
The energy level statistics of 2D electrons with spin-orbit scattering are considered near the disorder induced metal-insulator transition. Using the Ando model, the nearest-level-spacing distribution is calculated numerically at the…