相关论文: Surface critical exponents for a three-dimensional…

We study $(1+1)$-dimensional $SU(N)$ spin systems in the presence of the global $SU(N)$ rotation and lattice translation symmetries. By matching the mixed anomaly of the $PSU(N)\times\mathbb{Z}$ symmetry in the continuum limit, we identify…

We describe two dimensional models with a metallic Fermi surface which display quantum phase transitions controlled by strongly interacting critical field theories below their upper critical dimension. The primary examples involve…

The critical indices alpha', beta, gamma' and delta of the Quark Gluon Bags with Surface Tension Model with the tricritical and critical endpoint are calculated as functions of the usual parameters of this model and two newly introduced…

We study the special point in the phase diagram of a semi-infinite system, where the bulk transition is in the three-dimensional Ising universality class. To this end we perform a finite size scaling study of the improved Blume-Capel model…

Let $S$ be a punctured Riemann surface with Euler characteristic $\chi(S)<0$. For any unitary representation $\rho: \pi_1(S) \to U(N)$, we introduce its renormalized energy and its harmonic representatives, which are equivariant harmonic…

We report on a high statistics numerical study of the crystalline random surface model with extrinsic curvature on lattices of up to $64^2$ points. The critical exponents at the crumpling transition are determined by a number of methods all…

We consider critical points of the spherical pure $p$-spin spin glass model with Hamiltonian…

We analyze the landscape of general smooth Gaussian functions on the sphere in dimension $N$, when $N$ is large. We give an explicit formula for the asymptotic complexity of the mean number of critical points of finite and diverging index…

Recently, Auffinger, Ben Arous, and \v{C}ern\'y initiated the study of critical points of the Hamiltonian in the spherical pure $p$-spin spin glass model, and established connections between those and several notions from the physics…

The critical behavior at the ordinary transition in semi-infinite n-component anisotropic cubic models is investigated by applying the field theoretic approach in d=3 dimensions up to the two-loop approximation. Numerical estimates of the…

Liebmann's Theorem asserts that a compact, connected, convex surface with constant mean curvature (CMC) in the Euclidean space must be a totally umbilical sphere. In this article we extend Liebmann's result to hypersurfaces with boundary.…

Given a closed Riemannian manifold $(M^{n+1},g)$,$3\leq n+1\leq7$.In this paper,we will prove that for any $c>0$,suppose the number of closed $c-CMC$ hypersurfaces is finite,then there exists a metric $h$ on $M$ such that the $c-CMC$…

We study the effects of curved background geometries on the critical behavior of scalar field theory. In particular we concentrate on two maximally symmetric spaces: $d$-dimensional spheres and hyperboloids. In the first part of the paper,…

Let $(M,g)$ be a compact Riemann surface with unit area. We investigate the mean field equation for equilibrium turbulence: \begin{align} \begin{cases} -\Delta u = \rho_1\left(\frac{h_1e^{u}}{\int_Mh_1e^udv_g}-1\right) -…

In this paper, by using a special Euler-Ramanujan identity and the idea of Wick rotation, we show that a one-parameter family of solutions to the zero mean curvature equation in Lorentz-Minkowski $3$-space $\mathbb E_1^3$, namely…

We study the global behavior of (weakly) stable constant mean curvature hypersurfaces in general Riemannian manifolds. By using harmonic function theory, we prove some one-end theorems which are new even for constant mean curvature…

A strengthened canonical quantization scheme for the constrained motion on a curved hypersurface is proposed with introduction of the second category of fundamental commutation relations between Hamiltonian and positions/momenta, whereas…

In this work it is studied the Schr\"odinger equation for a non-relativistic particle restricted to move on a surface $S$ in a three-dimensional Minkowskian medium $\mathbb{R}_1^3$, i.e., the space $\mathbb{R}^3$ equipped with the metric…

In this work we give a method for constructing a one-parameter family of complete CMC-1 (i.e. constant mean curvature 1) surfaces in hyperbolic 3-space that correspond to a given complete minimal surface with finite total curvature in…

We study an approximate renormalization-group transformation to analyze the breakup of invariant tori for three degrees of freedom Hamiltonian systems. The scheme is implemented for the spiral mean torus. We find numerically that the…