Related papers: Nonlinear Sigma Models with Compact Hyperbolic Tar…
We investigate the topological theory obtained by twisting the N=(2,2) supersymmetric nonlinear sigma model with target a bihermitian space with torsion. For the special case in which the two complex structures commute, we show that the…
The topological properties of non-Hermitian Hamiltonian is a hot topic, and the theoretical studies along this research line are usually based on the two-level non-Hermitian Hamiltonian (or, equivalently, a spin-$1/2$ non-Hermitian…
Motivated by the recent interest in the criticality of open quantum many-body systems, we study nonlinear sigma models with complexified couplings as a general framework for nonunitary field theory. Applying the perturbative…
We have investigated the phase transition properties of classical linear sigma model. The fields were kept in contact with a heat bath for sufficiently long time such that fields are equilibrated at the temperature of the heat bath. It was…
A fundamental dichotomous classification for all physical systems is according to whether they are spinless or spinful. This is especially crucial for the study of symmetry-protected topological phases, as the two classes have distinct…
In a system of interacting thin rigid rods of equal length $2 \ell$ on a two-dimensional grid of lattice spacing $a$, we show that there are multiple phase transitions as the coupling strength $\kappa=\ell/a$ and the temperature are varied.…
We classify topological phases of non-Hermitian systems in the Altland-Zirnbauer classes with an additional reflection symmetry in all dimensions. By mapping the non-Hermitian system into an enlarged Hermitian Hamiltonian with an enforced…
The thermodynamic properties of vector (O(2) and Complex Spherical) models with four-body interactions are analyzed. When defined in dense topologies, these are effective models for the nonlinear interaction of scalar fields in the presence…
We construct N=2 supersymmetric nonlinear sigma models on the cotangent bundles over the non-compact exceptional Hermitian symmetric spaces M=E_{6(-14)}/SO(10)xU(1) and E_{7(-25)}/E_6xU(1). In order to construct them we use the projective…
Despite the extreme simplicity in their definition, spin glasses disclose a wide variety of non-trivial behaviors that are not yet fully understood. In this thesis we try to shed light on some of them, focusing on one hand on the search of…
The large-$N$ nonlinear $O(N)$, $CP^{N-1}$ $\sigma$ models are studied on $R^2 \times S^1$. The $N$-components scalar fields of the models are supposed to acquire a phase $e^{i2\pi\delta}$ $(0\leq \delta <1)$, along the circulation of the…
We discuss the thermodynamics of the O(3) nonlinear sigma model in 1+1 dimensions at nonzero chemical potential (equivalent to a magnetic field). In its conventional field theory representation the model suffers from a sign problem. By…
We use geometric arguments to derive a possible form for the radial part of the ``zero-mode Hamiltonian'' for the two dimensional sigma model with target space S^3, or more generally a compact simply connected Lie group.
In this succinct note, it is showed that a partition function of equivalent classes of hyperbolic surfaces can be connected to an Ising model located on the boundary of the Poincare disc, as hinted by Poincare's Uniformization theorem and…
We consider self-dual transverse-field Ising spin chains with $m$-spin interaction, where the phase transition is of second and first order, for m <= 3 and m>3, respectively. We present a statistical analysis of the spectra of the…
Non-Hermitian systems can host topological states with novel topological invariants and bulk-edge correspondences that are distinct from conventional Hermitian systems. Here we show that two unique classes of non-Hermitian 2D topological…
We study the renormalization of an N = 1 supersymmetric Lifshitz sigma model in three dimensions. The sigma model exhibits worldvolume anisotropy in space and time around the high-energy z = 2 Lifshitz point, such that the worldvolume is…
High temperature series expansions of the spin-spin correlation function for the plane rotator (or XY) model on the square lattice are extended by three terms through order $\beta^{20}$. Tables of the expansion coefficients are reported for…
The current paper is a short review of rigorous results for the 1-2 model. The 1-2 model on the hexagonal lattice is a model of statistical mechanics in which each vertex is constrained to have degree either 1 or 2. It was proposed in a…
In bosonic field theories the low-energy scattering of solitons that saturate Bogomol'nyi-type bounds can be approximated as geodesic motion on the moduli space of static solutions. In this paper we consider the analogous issue within the…