We discuss a new cluster representation for the internal energy and the specific heat of the d-dimensional Ising model , obtained by studying the percolation mapping of an Ising model with an arbitrary set of antiferromagnetic links. Such a representation relates the thermal operators to the topological properties of the Fortuin-Kasteleyn clusters of Ising percolation and is a powerful tool to ...

We solve the spin-1 quantum Ising model with single-ion anisotropy by mapping it onto a series of segmented spin-1/2 transverse Ising chains, separated by the S(z)=0 states called holes. A recursion formula is derived for the partition function to simplify the summation of hole configurations. This allows the thermodynamic quantities of this model to be rigorously determined in the thermodynami...

We define a new percolation model by generalising the FK representation of the Ising model, and show that on the triangular lattice and at high temperatures, the critical point in the new model corresponds to the Ising model. Since the new model can be viewed as Bernoulli percolation on a random graph, our result makes an explicit connection between Ising percolation and critical Bernoulli perc...

We give a generalization to an infinite tree geometry of Vidal’s infinite time-evolving block decimation (iTEBD) algorithm [4] for simulating an infinite line of quantum spins. We numerically investigate the quantum Ising model in a transverse field on the Bethe lattice using the Matrix Product State ansatz. We observe a second order phase transition, with certain key differences from the trans...

We develop a transfer matrix method to compute exactly the spin-spin correlation functions ^s0sn& of Bethe lattice spin models in the external magnetic field h and for any temperature T . We first compute ^s0sn& for the most general spin-S Ising model, which contains all possible single-ion and nearest-neighbor pair interactions. This general spin-S Ising model includes the spin1 2 simple Ising...

We describe an algorithm for the numerical simulation of quantum spin and boson systems. The method is based on the Trotter decomposition in imaginary time and a decoupling by auxiliary Ising spins. It can be applied, in principle, to arbitrary ~random! spin systems, however, in general it suffers from the ‘‘minus-sign problem.’’ This problem is absent in the case of the Ising model in a transv...

We have found a simple criterion which allows for the straightforward determination of the order-disorder critical temperatures. The method reproduces exactly results known for the two dimensional Ising, Potts and Z(N < 5) models. It also works for the Ising model on the triangular lattice. For systems which are not selfdual our proposition remains an unproven conjecture. It predicts βc = 0.265...

We develop a transfer matrix method to compute exactly the spin-spin correlation functions < s0sn > of Bethe lattice spin models in the external magnetic field h and for any temperature T . We first compute < s0sn > for the most general spin S Ising model, which contains all possible single-ion and nearest-neighbor pair interactions. This general spin S Ising model includes the spin-1/2 simple ...

We study a large class of critical two-dimensional Ising models namely critical Z-invariant Ising models on periodic graphs, example of which are the classical Z, triangular and honeycomb lattice at the critical temperature. Fisher [Fis66] introduced a correspondence between the Ising model and the dimer model on a decorated graph, thus setting dimer techniques as a powerful tool for understand...