Related papers: Symmetry-allowed phase transitions realized by the…
We introduce a fully frustrated XY model with nearest neighbor (nn) and next nearest neighbor (nnn) couplings which can be realized in Josephson junction arrays. We study the phase diagram for $0\leq x \leq 1$ ($x$ is the ratio between nnn…
We present an exact solution of the q-state Potts model on a class of generalized Sierpinski fractal lattices. The model is shown to possess an ordered phase at low temperatures and a continuous transition to the high temperature disordered…
Octahedral antiferromagnets are distinguished by crystal lattices composed of octahedra of magnetic ions. In the fully frustrated case, the Heisenberg Hamiltonian can be represented as a sum of squares of total spins for each octahedral…
Exact results in frustrated quantum many-body systems are rare, especially in dimensions higher than one. The Shastry-Sutherland (SS) model stands out as a rare example of a two-dimensional spin system with an exactly solvable dimer singlet…
Geometric frustration is recognized to generate complex morphologies in self-assembling particulate and molecular systems. In bulk states, frustrated drives structured arrays of topological defects. In the dilute limit, these systems have…
We argue that ground states of 1D spin chains can spontaneously break U(1) ``easy-plane'' spin rotation symmetry, via true long-range order of $(S^x, S^y)$, at the phase transition between two quasi-long-range-ordered phases. The critical…
The phase diagram of the $\mathbb{Z}(5)$ spin model is studied numerically on the square lattice by means of the {\sl Density Matrix Renormalization Group}. In the regime where the two nearest-neighbor couplings have opposite signs, a…
The intermediate 3D XY scaling theory of superconductivity at zero and nonzero magnetic fields is developed, based only upon the dimensional hypothesis $B\sim (Length)^{-2}$. Universal as well as nonuniversal aspects of the theory are…
Using mean-field theory and high resolution Monte Carlo simulation technique based on multi-histogram method, we have investigated the critical properties of an antiferromagnetic XY model on the 2D Kagom\'e lattice, with single ion…
We investigate the one-dimensional finite-size XY model with opposing surface fields in the X direction. Exact solutions are obtained for the two-site and three-site models, while numerical methods are employed for models with more than…
Transport measurements are carried out on dice Josephson-junction arrays with the frustration index $f=1/3$ and 1/2 which possess, within the limit of the $XY$ model, an accidental degeneracy of the ground states as a consequence of the…
We present in this chapter a review on recent numerical studies dealing with frustrated vector spin systems in two and three dimensions.
Three 2D spin models made of frustrated zig-zag chains with competing interactions which by exact summation with respect to some degrees of freedom can be replaced by an effective temperature-dependent interaction were considered. The first…
We carry out extensive Monte Carlo simulations of the three-dimensional (3D) uniformly frustrated XY model with uncorrelated randomly perturbed couplings, as a model for the equilibrium behavior of an extreme type-II superconductor with…
In clean enough samples of the high-$T_c$ oxide materials, the phase transition into the superconducting state occurs along a first order line in the $H$-$T$ plane. This means that a two-phase region occurs in the B-$T$ plane, in which the…
We examine the ground state of a Heisenberg model with arbitrary spin S on a one-dimensional lattice composed of diamond-shaped units. A unit includes two types of antiferromagnetic exchange interactions which frustrate each other. The…
The properties of a dilute Ising magnet are studied using a two-dimensional spin-pseudospin model with charged impurities and a frustration caused by the competition of the charge and magnetic orderings. Based on the classical Monte Carlo…
The universal behaviour of two-dimensional loop models can change dramatically when loops are allowed to cross. We study models with crossings both analytically and with extensive Monte Carlo simulations. Our main focus (the 'completely…
The ground state phase diagram of the frustrated ferromagnetic spin-1/2 chain is investigated using the exact diagonalization technique. It is shown that there is a jump in the spontaneous magnetization and the ground state of the system…
We investigate a spin-$1/2$ two-leg honeycomb ladder with frustrating next-nearest-neighbor (NNN) coupling along the legs, which is equivalent to two $J_1$-$J_2$ spin chains coupled with $J_\perp$ at odd rungs. The full parameter region of…