Related papers: Number-Rigidity and $\beta$-Circular Riesz gas
The one-loop effective potential for non-relativistic bosons with a delta function repulsive potential is calculated for a given chemical potential using functional methods. After renormalization and at zero temperature it reproduces the…
The thermodynamic formalism expresses chaotic properties of dynamical systems in terms of the Ruelle pressure $\psi(\beta)$. The inverse-temperature like variable $\beta$ allows one to scan the structure of the probability distribution in…
We present measurements of the orientation $\theta_0$ and temperature amplitude $\delta$ of the large-scale circulation in a cylindrical sample of turbulent Rayleigh-Benard convection (RBC) with aspect ratio $\Gamma \equiv D/L = 1.00$ ($D$…
Let $M$ be a complete non-compact manifold satisfying the volume doubling condition, with doubling index $N$ and reverse doubling index $n$, $n\le N$, both for large balls. Assume a Gaussian upper bound for the heat kernel, and an…
We present a uniqueness result for Gibbs point processes with interactions that come from a non-negative pair potential; in particular, we provide an explicit uniqueness region in terms of activity $z$ and inverse temperature $\beta$. The…
The critical behavior of the two-dimensional N-vector cubic model is studied within the field-theoretical renormalization-group (RG) approach. The beta-functions and critical exponents are calculated in the five-loop approximation, RG…
We propose a definition of vorticity at inverse temperature \beta for Gibbs states in quantum XY spin systems on the lattice by testing \exp[-\beta H] on a complete set of observables ("one-point functions"). We show in particular that it…
The repulsive Lieb-Liniger model can be obtained as the non-relativistic limit of the Sinh-Gordon model: all physical quantities of the latter model (S-matrix, Lagrangian and operators) can be put in correspondence with those of the former.…
We propose a definition of vorticity at inverse temperature $\beta$ for Gibbs states in quantum XY or Heisenberg spin systems on the lattice by testing $\exp[-\beta H]$ on a complete set of observables ("one-point functions"). Imposing a…
We prove an upper bound for the free energy (per unit volume) of the dilute Bose gas in the thermodynamic limit, showing that the free energy at density $\rho$ and inverse temperature $\beta$ differs from that of the non-interacting system…
We consider a new class of unconventional critical phenomena that is characterized by singularities only in dynamical quantities and has no thermodynamic signatures. A possible example is the recently proposed many-body localization…
We prove the Gibbs variational principle for the Asakura--Oosawa model in which particles of random size obey a hardcore constraint of non-overlap and are additionally subject to a temperature-dependent area interaction. The particle size…
While the Gross--Pitaevskii equation is well-established as the canonical dynamical description of atomic Bose-Einstein condensates (BECs) at zero-temperature, describing the dynamics of BECs at finite temperatures remains a difficult…
We study the boundedness on $L^p$ of the Riesz transform $\nabla L^{-1/2}$, where $L$ is one of several operators defined on $\R$ or $\R_+$, endowed with the measure $r^{d-1} dr$, $d > 1$, where $dr$ is Lebesgue measure. For integer $d$,…
We consider a one-dimensional continuum gas of pointlike positive and negative unit charges interacting via a logarithmic potential. The mapping onto a two-dimensional boundary sine-Gordon field theory with zero bulk mass provides the full…
The formalism of Ursell operators provides a self-consistent integral equation for the one-particle reduced operator. In three dimensions this technique yields values of the shift in the Bose-Einstein condensation (BEC) transition…
This is the second paper in a series studying the global asymptotics of discrete $N$-particle systems with inverse temperature parameter $\theta$ in the high temperature regime. In the first paper, we established necessary and sufficient…
We prove, for any $\beta >0$, a central limit theorem for the fluctuations of linear statistics in the Sine-$\beta$ process, which is the infinite volume limit of the random microscopic behavior in the bulk of one-dimensional log-gases at…
Zeros of the $n$th moment of the partition function $[Z^n]$ are investigated in a vanishing temperature limit $\beta \to \infty$, $n \to 0$ keeping $y=\beta n \sim O(1)$. In this limit, the moment parameterized by $y$ characterizes the…
We complete the verification of the 1952 Yang and Lee proposal that thermodynamic singularities are exactly the limits in ${\mathbb R}$ of finite-volume singularities in ${\mathbb C}$. For the Ising model defined on a finite…