Related papers: The complexity of spherical p-spin models - a seco…
A pinch point singularity in the structure factor characterizes an important class of condensed matter that is a counterpoint to the paradigm of broken symmetry. This class includes water ice, charge ice and spin ice. Of these, dipolar spin…
We prove an asymptotic formula for the second moment of automorphic L-functions of even weight and prime power level. The error term is estimated uniformly in all parameters: level, weight, shift and twist.
The quantum S=1 spin model on the spatially anisotropic triangular lattice is investigated numerically. The nematic and valence-bond-solid (VBS) phases are realized by adjusting the spatial anisotropy and the biquadratic interaction. The…
Moment evaluations are important for the study of non-classical orthogonal polynomial systems for which explicit representations are not known. In this paper we compute, in terms of the hypergeometric function, the moments associated with a…
We study the asymptotic behavior of large data solutions to Schr\"odinger equations $i u_t + \Delta u = F(u)$ in $\R^d$, assuming globally bounded $H^1_x(\R^d)$ norm (i.e. no blowup in the energy space), in high dimensions $d \geq 5$ and…
In this article, we analyse an integral equation of the second kind that represents the solution of $N$ interacting dielectric spherical particles undergoing mutual polarisation. A traditional analysis can not quantify the scaling of the…
In general relativity, the Einstein equations provide spherically symmetric static spacetimes with dynamics defined as an evolution along the radial coordinate $r$. The geometrical sector becomes a one-dimensional mechanical system, with…
Recent tensor-network samplings of modified Nishimori spin glasses have revealed robust finite-temperature critical transitions in two dimensions, defying the standard Edwards-Anderson lower critical dimension boundary ($d_{l}\approx2.5$).…
We propose an integrable model of the spin-1/2 Heisenberg chain coupled to two impurity moments. With the open boundary conditions at the impurity sites, the model can be exactly solved for arbitrary impurity spin and arbitrary exchange…
Given a solution $u$ to a linear homogeneous second order elliptic equation with Lipschitz coefficients, we introduce techniques for giving improved estimates of the critical set $\Cr(u)\equiv \{x:|\nabla u|(x)=0\}$. The results are new…
We consider the supercritical problem {equation*} -\Delta u=|u| ^{p-2}u\text{\in}\Omega,\quad u=0\text{\on}\partial\Omega, {equation*} where $\Omega$ is a bounded smooth domain in $\mathbb{R}^{N}$ and $p$ smaller than the critical exponent…
We study the non-equilibrium relaxation of the spherical spin-glass model with p-spin interactions in the $N \rightarrow \infty$ limit. We analytically solve the asymptotics of the magnetization and the correlation and response functions…
We formulate and analyze the Hamiltonian dynamics of a pair of massive spinless point particles in (2+1)-dimensional Einstein gravity by anchoring the system to a conical infinity, isometric to the infinity generated by a single massive but…
We consider Gaussian random monochromatic waves $u$ on the plane depending on a real parameter $s$ that is directly related to the regularity of its Fourier transform. Specifically, the Fourier transform of $u$ is $f\,d\sigma$, where…
The emergence of a collective behavior in a many-body system is responsible of the quantum criticality separating different phases of matter. Interacting spin systems in a magnetic field offer a tantalizing opportunity to test different…
We continue our study of the gravitational collapse of spherically symmetric skyrmions. For certain families of initial data, we find the discretely self-similar Type II critical transition characterized by the mass scaling exponent $\gamma…
Exact results of the finite-size behavior of the susceptibility in three-dimensional mean spherical model films under Dirichlet-Dirichlet, Dirichlet-Neumann and Neumann-Neumann boundary conditions are presented. The corresponding scaling…
Making use of integral representations, we develop a unified approach to establish blow up profiles, compactness and existence of positive solutions of the conformally invariant equations $P_\sigma(v)= Kv^{\frac{n+2\sigma}{n-2\sigma}}$ on…
We analyze models of spin glasses on the two-dimensional square lattice by exploiting symmetry arguments. The replicated partition functions of the Ising and related spin glasses are shown to have many remarkable symmetry properties as…
The criticality between the nematic and valence-bond-solid (VBS) phases was investigated for the two-dimensional quantum S=1-spin model with the three-spin and biquadratic interactions by means of the numerical diagonalization method. It is…