Related papers: On the relationship between sigma models and spin …
The renormalization constants present in the lattice evaluation of the topological susceptibility can be non-perturbatively calculated by using the so-called heating method. We test this method for the $O(3)$ non-linear $\sigma$-model in…
We analyze cubic spin 3 interaction in AdS space using the higher spin extension of string-theoretic sigma-model constructed in our previous work, which low energy limit is described by AdS vacuum. We find that, in the leading order of the…
We analyze two extended versions [the Ishimori model (IM) and a related system, which will be called modified Ishimori model (mIM)] of the continuous Heisenberg model in (2+1)-dimensions within the complex Hirota scheme. The IM, proposed in…
Building a multi-field theory with canonical and non-canonical contributions, one studies the topological solitons of the O(3)-sigma model. We propose a model constituted by the O(3)-sigma field, the cuscuton-like neutral scalar field, and…
A unidirectional "density" wave order in an otherwise isotropic environment is guaranteed to display a smecticlike Goldstone mode. Examples of such "soft" states include conventional smectic liquid crystals, putative…
We analyse the low temperature properties of a system of classical Heisenberg spins on a hexagonal lattice with Kitaev couplings. For a lattice of 2N sites with periodic boundary conditions, we show that the ground states form an (N+1)…
We discuss a new strategy for treating the complex action problem of lattice field theories with a $\theta$-term based on density of states (DoS) methods. The key ingredient is to use open boundary conditions where the topological charge is…
We review the construction of exactly solvable lattice models whose continuum limits are $N=2$ supersymmetric models. Both critical and off-critical models are discussed. The approach we take is to first find lattice models with natural…
We describe a topological field theory that studies the moduli space of solutions of the symplectic vortex equations. It contains as special cases the topological sigma-model and topological Yang-Mills over Kahler surfaces. The correlation…
For the classical N-vector model, with arbitrary N, we have computed through order \beta^{17} the high temperature expansions of the second field derivative of the susceptibility \chi_4(N,\beta) on the simple cubic and on the body centered…
We study the massless Schwinger model with an additional 4-fermi interaction and a topological term. For topological angle $\theta = \pi$ charge conjugation symmetry is implemented in a non-trivial way and we study the possibility of its…
We present a full identification of lattice model properties with their field theoretical counter parts in the continuum limit for a supersymmetric model for itinerant spinless fermions on a one dimensional chain. The continuum limit of…
We introduce the concept of super universality in quantum Hall and spin liquids which has emerged from previous studies. It states that all the fundamental features of the quantum Hall effect are generically displayed as general topological…
We have studied the diluted Heisenberg spin glass model in a 3-component random field for the commonly-used one-dimensional long-range model where the probability that two spins separated by a distance $r$ interact with one another falls as…
By analytic continuation to real theta of data obtained from numerical simulation at imaginary theta we study the Haldane conjecture and show that the O(3) non-linear sigma model with a theta term in 2 dimensions becomes massless at…
We carry out both the tight-binding model and the $ab\ initio$ to study the layered silicene, the spin, valley, sublattice degrees of freedom are taken into consider and the effects of electric field, magnetic field, and even the light in…
We consider the Ashkin-Teller model on the square lattice, which is represented by two Ising models ($\sigma$ and $\tau$) having a four-spin coupling of strength, $\epsilon$, between them. We introduce an asymmetric defect line in the…
We consider renormalization of effective field theory interactions by discretizing the continuum on a tight-binding lattice. After studying the one-dimensional problem, we address s-wave collisions in three dimensions and relate the bare…
A lattice approach is developed to measure the sphaleron free energy. Its feasibility is demonstrated through a Monte Carlo study of the two-dimensional O(3) sigma model.
Topological phases protected by symmetry can occur in gapped and---surprisingly---in critical systems. We consider non-interacting fermions in one dimension with spinless time-reversal symmetry. It is known that the phases are classified by…