Related papers: Virial expansion and TBA in O(N) sigma models
A variational approach for the free energy is used to study the three-dimensional anisotropic XY model in the presence of a crystal field. The magnetization and the phase diagrams as a function of the parameters of the Hamiltonian are…
We study the UV properties of the three-dimensional ${\cal N}=4$ SUSY nonlinear sigma model whose target space is $T^*(CP^{N-1})$ (the cotangent bundle of $CP^{N-1}$) to higher orders in the 1/N expansion. We calculate the $\beta$-function…
We derive a sharp spectral estimate for a superlinear free boundary problem arising in plasma physics. The semilinear equation is coupled with a constraint, which forces the analysis of a non-local eigenvalue equation. Consequently the…
In this paper, we explore a new class of integrable sigma models, which we refer to as the "dual regime" of Yang-Baxter (YB) deformed $\mathrm{O}(2N)$ sigma models. This dual regime manifests itself in the conformal perturbation approach.…
Using a simple identity between various partial derivatives of the energy of the vector model in 0+0 dimensions, we derive explicit results for the coefficients of the large N expansion of the model. These coefficients are functions in a…
We present a method, based on loop equations, to compute recursively all the terms in the large $N$ topological expansion of the free energy for the 2-hermitian matrix model. We illustrate the method by computing the first subleading term,…
The validity of the renormalization group approach for large $N$ is clarified by using the vector model as an example. An exact difference equation is obtained which relates free energies for neighboring values of $N$. The reparametrization…
We consider the statistical mechanics of a classical particle in a one-dimensional box subjected to a random potential which constitutes a Wiener process on the coordinate axis. The distribution of the free energy and all correlation…
We analyse the noncommutative U(1) sigma model, which arises from the vacuum dynamics of the noncommutative charged tachyonic field. The sector of ``spherically symmetric'' excitations of the model is equivalent to a chain of rotators.…
We compute effective energies of thin bilayer structures composed by soft nematic elastic-liquid crystals in various geometrical regimes and functional configurations. Our focus is on order-strain interaction in elastic foundations composed…
We study a three dimensional conformal field theory in terms of its partition function on arbitrary curved spaces. The large $N$ limit of the nonlinear sigma model at the non-trivial fixed point is shown to be an example of a conformal…
We discuss and illustrate through numerical examples the relations between generating functionals, thermodynamic consistency (in particular the virial-free energy one), and uniqueness of the solution, in the integral equation theory of…
In this paper we study the integrability of a family of models with U(1)xSU(N) symmetry. They admit fermionic and bosonic formulations related through bosonization and subsequent T-duality. The fermionic theory is just the CP^(N-1) sigma…
We provide accurate Monte Carlo results for the free energy of interfaces with periodic boundary conditions in the 3D Ising model. We study a large range of inverse temperatures, allowing to control corrections to scaling. In addition to…
We prove a number of results concerning the large $N$ asymptotics of the free energy of a random matrix model with a polynomial potential $V(z)$. Our approach is based on a deformation $\tau_tV(z)$ of $V(z)$ to $z^2$, $0\le t<\infty$ and on…
We develop a perturbative approach to study the supersymmetric non-linear sigma model characterized by a generic coupling matrix in the strong coupling limit. The method allows us to calculate explicitly the moments of the eigenfunctions…
We introduce modes of instantaneous optimal growth of free energy for the fully electromagnetic gyrokinetic equations. We demonstrate how these "optimal modes" arise naturally from the free energy balance equation, allowing its convenient…
We derive the Wilsonian renormalization group equation in two dimensional ${\cal N}=2$ supersymmetric nonlinear sigma models. This equation shows that the sigma models on compact Einstein K\"{a}hler manifolds are aymptotically free. This…
We investigate the enlarged class of open finite strings in $(2+1)D$ space-time. The new dynamical system related to this class is constructed and quantized here. As the result, the energy spectrum of the model is defined by a simple…
We find the free-energy in the thermodynamic limit of a one dimensional XY model associated to a system of N qubits. The coupling among the sigma_i^z is a long range two bodies random interaction. The randomness in the couplings is the…