Related papers: Surface critical exponents for a three-dimensional…

Modifications of baryon properties due to the restoration of the chiral symmetry in an external hot and dense baryon medium are investigated in an effective chiral quark-meson theory. The nucleon arises as a soliton of the Gell-Mann -…

We investigate surfaces with constant harmonic-mean curvature one (HMC-1 surfaces) in hyperbolic three-space. We allow them to have certain kinds of singularities, and discuss some global properties. As well as flat surfaces and surfaces…

For a harmonic map $u:M^3\to S^1$ on a closed, oriented $3$--manifold, we establish the identity $$2\pi \int_{\theta\in S^1}\chi(\Sigma_{\theta})\geq \frac{1}{2}\int_{\theta\in S^1}\int_{\Sigma_{\theta}}(|du|^{-2}|Hess(u)|^2+R_M)$$ relating…

We consider random q-state Potts models for $3\le q \le 8$ on the square lattice where the ferromagnetic couplings take two values $J_1>J_2$ with equal probabilities. For any q the model exhibits a continuous phase transition both in the…

In this article, we consider compact surfaces $\Sigma$ having constant mean curvature $H$ ($H$-surfaces) whose boundary $\Gamma=\partial\Sigma\subset \mathbb{M}_0= \mathbb{M} \times_f\{0\}$ is transversal to the slice $\mathbb{M}_0$ of the…

Considering the kinematics of the moving frame associated with a constant mean curvature surface immersed in S^3 we derive a linear problem with the spectral parameter corresponding to elliptic sinh-Gordon equation. The spectral parameter…

We consider the following singularly perturbed elliptic problem $$ \varepsilon^2\triangle\tilde{u}-\tilde{u}+\tilde{u}^p=0, \ \tilde{u}>0\quad \mbox{in} \ \Omega,\ \ \ \frac{\partial\tilde{u}}{\partial \mathbf{n}}=0 \quad \mbox{on}\…

We consider a holographic model of QCD at finite temperature with nonzero chemical potentials conjugate to $R$-charge densities. A critical surface of the confinement-deconfinement phase transition is shown for five-dimensional charged…

In ferromagnetic spin models above the critical temperature ($T > T_{cr}$) the partition function zeros accumulate at complex values of the magnetic field ($H_E$) with a universal behavior for the density of zeros $\rho (H) \sim | H - H_E…

Consider the classical $(2+1)$-dimensional Solid-On-Solid model above a hard wall on an $L\times L$ box of $\bbZ^2$. The model describes a crystal surface by assigning a non-negative integer height $\eta_x$ to each site $x$ in the box and 0…

Using the local potential approximation of the exact renormalization group (RG) equation, we show the various domains of values of the parameters of the O(1)-symmetric scalar Hamiltonian. In three dimensions, in addition to the usual…

Let $M^{n+1}$ be a closed manifold of dimension $3\le n+1\le 7$ equipped with a generic Riemannian metric $g$. Let $c$ be a positive number. We show that, either there exist infinitely many distinct closed hypersurfaces with constant mean…

We prove a Chern-Lashof type formula computing the expected number of critical points of smooth function on a smooth manifold $M$ randomly chosen from a finite dimensional subspace $V\subset C^\infty(M)$ equipped with a Gaussian probability…

We study the critical behavior of the 3-state Potts model, where the spins are located at the centers of the occupied squares of the deterministic Sierpinski carpet. A finite-size scaling analysis is performed from Monte Carlo simulations,…

A Monte Carlo (MC) study is performed to evaluate the surface tension $\gamma $ of spherical membranes that may be regarded as the models of the lipid layers. We use the canonical surface model defined on the self-avoiding triangulated…

By mapping the hamiltonian of the spin one ferromagnet onto that of the classical spherical model we investigate the possible phase transitions and the phase diagram of the spin one ferromagnet. Similarly to what happens in the spherical…

For all $N \geq 9$, we find smooth entire epigraphs in $\R^N$, namely smooth domains of the form $\Omega : = \{x\in \R^N\ / \ x_N > F (x_1,\ldots, x_{N-1})\}$, which are not half-spaces and in which a problem of the form $\Delta u + f(u) =…

We revisit the Schr\"{o}dinger equation of a quantum particle that is confined on a curved surface. Inspired by the novel work of R. C. T. da Costa [1] we find the field equation in a more convenient notation. The contribution of the…

We prove the existence of smooth closed hypersurfaces of prescribed mean curvature homeomorphic to $S^n$ for small $n, n\le6$, provided there are barriers.

We prove the existence of a smooth complete $3$-convex hypersurface which satisfies prescribed curvature equation $\prod\limits_{i = 1}^n (H - \kappa_i) = \big( (n - 1) \sigma \big)^n$ for $n = 4$ and has prescribed asymptotic boundary…