相关论文: The mother body phase transition in the normal mat…
We consider an $\varepsilon$-periodic ($\varepsilon\to 0$) tubular structure, modelled as a magnetic Laplacian on a metric graph, which is periodic along a single axis. We show that the corresponding Hamiltonian admits norm-resolvent…
We consider the two matrix model with an even quartic potential W(y)=y^4/4+alpha y^2/2 and an even polynomial potential V(x). The main result of the paper is the formulation of a vector equilibrium problem for the limiting mean density for…
We consider the hermitian random matrix model with external source and general polynomial potential, when the source has two distinct eigenvalues but is otherwise arbitrary. All such models studied so far have a common feature: an…
We study semilinear elliptic equations with Hardy potential $\mathrm{(E)} \; -L_\mu u+u^q=0$ in a bounded smooth domain $\Omega\subset \mathbb R^N$. Here $q>1$, $L_\mu=\Delta+\frac{\mu}{\delta_\Omega^2}$ and…
We use the numerical renormalization group method to investigate the spectral properties of a single-impurity Anderson model with a gap {\delta} across the Fermi level in the conduction-electron spectrum. For any finite {\delta} > 0, at…
We identify a quantum critical point with fractal symmetry whose effective theory eludes the renormalization group framework. We consider the Newman-Moore model with three-body interaction subjected to an external transverse field, which…
Quantum many-body systems undergoing phase transitions have been proposed as probes enabling beyond-classical enhancement of sensing precision. However, this enhancement is usually limited to a very narrow region around the critical point.…
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 study the spectrum of phase transitions with prescribed mean curvature in Riemannian manifolds. These phase transitions are solutions to an inhomogeneous semilinear elliptic PDE that give rise to diffuse objects (varifolds) that limit to…
Describing the deviation of a real structure from a hypothetical higher-symmetry ideal can be a powerful tool to understand and interpret phase transitions. Here we introduce a simple yet effective metric that quantifies the degree of unit…
Several Riemannian metrics and families of Riemannian metrics were defined on the manifold of Symmetric Positive Definite (SPD) matrices. Firstly, we formalize a common general process to define families of metrics: the principle of…
We construct and analyze the phase diagram of a self-interacting matrix field in two dimensions coupled to the curvature of the non-commutative truncated Heisenberg space. In the infinite size limit, the model reduces to the renormalizable…
We formulate and study a class of U(N)-invariant quantum mechanical models of large normal matrices with arbitrary rotation-invariant matrix potentials. We concentrate on the U(N) singlet sector of these models. In the particular case of…
The electroweak phase transition is investigated by means of the perturbatively calculated high temperature effective potential. An analytic result to order $g^4,\lambda^2$ is presented for the Abelian Higgs model, the SU(2)-Higgs model and…
We present, theoretical predictions and Monte Carlo simulations, for a simple three matrix model that exhibits an exotic phase transition. The nature of the transition is very different if approached from the high or low temperature side.…
This paper deals with some mathematical models arising in the theory of epitaxial growth of crystal. We focalize the study on a stationary problem which presents some analytical difficulties. We study the existence of solutions. The central…
In quantum many-body system, dimensionality plays a critical role on type of the quantum phase transition. In order to study the quantum system during dimensional crossover, we studied the Bose-Hubbard model on cubic lattice with…
We study a one-dimensional quasiperiodic system described by the off-diagonal Aubry-Andr\'{e} model and investigate its phase diagram by using the symmetry and the multifractal analysis. It was shown in a recent work ({\it Phys. Rev. B}…
Although it is well-known that some exponential family random graph model (ERGM) families exhibit phase transitions (in which small parameter changes lead to qualitative changes in graph structure), the behavior of other models is still…
We consider a two-dimensional equilibrium measure problem under the presence of quadratic potentials with a point charge and derive the explicit shape of the associated droplets. This particularly shows that the topology of the droplets…