相关论文: Haagerup's phase transition at polydisc slicing
The effect of polydispersity on the freezing transition of hard spheres is examined within a moment description. At low polydispersities a single fluid-to-crystal transition is recovered. With increasing polydispersity we find a density…
Because of long-wavelength fluctuations, the nature of solids and phase transitions in 2D are different from those in 3D systems, and have been heavily debated in past decades, in which the focus was on the existence of hexatic phase. Here,…
When placed on an inclined plane, a perfect 2D disk or 3D sphere simply rolls down in a straight line under gravity. But how is the rolling affected if these shapes are irregular or random? Treating the terminal rolling speed as an order…
We present a Monte Carlo simulation study of the phase behavior of two-dimensional classical particles repelling each other through an isotropic Gaussian potential. As in the analogous three-dimensional case, a reentrant-melting transition…
The beta polytope $P_{n,d}^\beta$ is the convex hull of $n$ i.i.d. random points distributed in the unit ball of $\mathbb{R}^d$ according to a density proportional to $(1-\lVert{x}\rVert^2)^{\beta}$ if $\beta>-1$ (in particular, $\beta=0$…
Using a simple analytic approach, we study the universal properties of second-order phase transition in holographic superconductor models. We explore a general model in arbitrary dimensions in which the condensation occurs via the…
We consider overdamped Langevin diffusions in Euclidean space, with curvature equal to the spectral gap. This includes the Ornstein-Uhlenbeck process as well as non-Gaussian and non-product extensions with convex interaction, such as the…
We present a pedagogical review of the swelling thermodynamics and phase transitions of polymer gels. In particular, we discuss how features of the volume phase transition of the gel's osmotic equilibrium is analogous to other transitions…
Multiple electroweak phase transitions occurring sequentially in the early universe can give rise to intriguing phenomenology, compared to the typical single-step electroweak phase transition. In this work, we investigate this scenario…
We present numerical evidence of a critical-like transition in an out-of-equilibrium mean-field description of a quantum system. By numerically solving the Gross-Pitaevskii equation we show that quantum turbulence displays an abrupt change…
In order to characterize the higher order moments of the particle multiplicity, we implement the linear-sigma model with Polyakov-loop correction. We first studied the critical phenomena and estimated some thermodynamic quantities. Then, we…
This study investigates various phase transitions, including those of 2nd, 1st, and 0th order, in a holographic p-wave superfluid model incorporating 4th- and 6th-order nonlinear terms with coefficients $\lambda$ and $\tau$. We demonstrate…
We prove a Hausdorff dimension result for the image of two-dimensional multiplicative cascade processes, and we obtain from this result a KPZ-type formula which normally has one point of phase transition.
The existence of a second Higgs doublet in Nature could lead to a cosmological first order electroweak phase transition and explain the origin of the matter-antimatter asymmetry in the Universe. We explore the parameter space of such a…
We study in this work the dynamics of a collection of identical hollow spheres (ping-pong balls) that rest on a horizontal metallic grid. Fluidization is achieved by means of a turbulent air current coming from below. The upflow is adjusted…
Let $f$ be a holomorphic Hecke cusp form of weight $k$ for $\mathrm{SL}_2(\mathbb{Z})$, and let $(\lambda_f(n))_{n\geq1}$ denote its sequence of Hecke eigenvalues. We compute the first and second moments of the sums $S(x,f)=\sum_{x\leq…
In this work, three different particle sizes: the static radius $R_{s}$, hydrodynamic radius $R_{h}$ and apparent hydrodynamic radius $ R_{h,app}$ obtained using the light scattering technique, are investigated for dilute poly-disperse…
We introduce a simple generalization of the basic holographic superconductor model in which the spontaneous breaking of a global U(1) symmetry occurs via the Stueckelberg mechanism. This more general setting allows tuning features such as…
Using Monte Carlo simulations, we systematically investigate the effect of particle size distribution on the phase behaviour of polydisperse hard disks. Compared with the commonly used Gaussian-like polydisperse hard disks [Commun. Phys. 2,…
We establish a sharp moment comparison inequality between an arbitrary negative moment and the second moment for sums of independent uniform random variables, which extends Ball's cube slicing inequality.