相关论文: Vortex characterisation of frustration in the 2d I…

The frustrated Ising model in two dimensions is revisited. The frustration is quantified in terms of the number of non-trivial plaquettes which is invariant under the Nishimori gauge symmetry. The exact ground state energy is calculated…

We derive exact analytical expressions for the ground-state energy and entropy of the two-dimensional $\pm J$ Ising spin glass, uncovering a nested hierarchy of frustrations. Each level in this hierarchy contributes through the kernel and…

We consider discrete spin models on arbitrary planar graphs and lattices with frustrated interactions. We first analyze the Ising model with frustrated plaquettes. We use an algebraic approach to derive the result that an Ising model with…

A frustrated Ising model on a diamond hierarchical lattice is studied. We obtain the exact partition function of this model and calculate the transition temperature, specific heat, entropy, magnetization, and ferromagnetic correlation…

It is shown that the partition function of the 2d Ising model on the dual finite lattice with periodical boundary conditions is expressed through some specific combination of the partition functions of the model on the torus with…

We present a method to analyze magnetic properties of frustrated Ising spin models on specific hierarchical lattices with random dilution. Disorder is induced by dilution and geometrical frustration rather than randomness in the internal…

Here an artificial spin ice (ASI) lattice is introduced that exhibits unique Ising and non-Ising behavior under specific field switching protocols because of the inclusion of coupled nanomagnets into the unit cell. In the Ising regime, a…

After a short introduction on frustrated spin systems, we study in this chapter several two-dimensional frustrated Ising spin systems which can be exactly solved by using vertex models. We show that these systems contain most of the…

An exact algorithm is used to investigate the distributions of the degeneracies of low-energy excited states for the bimodal Ising spin glass on the brickwork lattice. Since the distributions are extreme and do not self-average, we base our…

We use Monte Carlo (MC) methods to simulate a two-dimensional (2D) bond-diluted Ising model on the square lattice which has frustration between the nearest-neighbor interaction J1 and the next-nearest-neighbor interaction J2. In this paper,…

The gauge glass model offers an interesting example of a randomly frustrated system with a continuous O(2) symmetry. In two dimensions, the existence of a glass phase at low temperatures has long been disputed among numerical studies. To…

In the presented article we present an algorithm for the computation of ground state spin configurations for the 2d random bond Ising model on planar triangular lattice graphs. Therefore, it is explained how the respective ground state…

We show that the two dimensional Ising model is complete, in the sense that the partition function of any lattice model on any graph is equal to the partition function of the 2D Ising model with complex coupling. The latter model has all…

The frustration properties of the Ising model on a one-dimensional monoatomic equidistant lattice are investigated taking into account the exchange interactions of atomic spins at the sites of the first (nearest), second (next-nearest) and…

We consider whether it is possible to find ground states of frustrated spin systems by solving them locally. Using spin glass physics and Imry-Ma arguments in addition to numerical benchmarks we quantify the power of such local solution…

The Ising model, often seen as the paradigmatic spin model, has been heavily studied for its mathematical description of ferromagnetism in statistical mechanics. We explore a quantum version of this model, the transverse field Ising model,…

The problem of N interacting spins on a lattice is equivalent to one of N clusters linked in a specific manner. The energy of any configuration of spins can be expressed in terms of the energy levels of this cluster. A new expression is…

In this paper, we performed the comprehensive studies of frustration properties in the Ising model on a decorated square lattice in the framework of an exact analytical approach based on the Kramers--Wannier transfer matrix method. The…

The geometric frustration of the spin-1/2 Ising-Heisenberg model on the triangulated Kagome (triangles-in-triangles) lattice is investigated within the framework of an exact analytical method based on the generalized star-triangle mapping…

The Ising spin glass in two dimensions exhibits rich behavior with subtle differences in the scaling for different coupling distributions. We use recently developed mappings to graph-theoretic problems together with highly efficient…