Related papers: Finite-lattice form factors in free-fermion models
The 3d Ising model on a regular cubic lattice can be expressed in terms of an SU(2) 2d fermionic model with a $Z_2$-fluxes. We modify the model such that it is defined on the dual to a body centered cubic lattice. The advantage of this…
A class of recently introduced su(n) `free-fermion' models has recently been used to construct generalized Hubbard models. I derive an algebra defining the `free-fermion' models and give new classes of solutions. I then introduce a…
We study classical Ising spin-$\frac{1}{2}$ models on the 2D square lattice with ferromagnetic or antiferromagnetic nearest-neighbor interactions, under the effect of a pure imaginary magnetic field. The complex Boltzmann weights of spin…
In this work, exact solutions are obtained for a class of generalized gauge-invariant $n$-chain Ising models ($n=1,2,3,4$) with arbitrary multi-spin interactions that are invariant under the local $\mathbb{Z}_2$ gauge group. On a strip…
We analyze free-fermion conditions on vertex models. We show --by examining examples of vertex models on square, triangular, and cubic lattices-- how they amount to degeneration conditions for known symmetries of the Boltzmann weights, and…
Using techniques from hopping expansion we identically map the lattice Schwinger model with Wilson fermions to a model of oriented loops on the lattice. This is done by first computing the explicit form of the fermion determinant in the…
We review problems involving the use of Grassmann techniques in the field of classical spin systems in two dimensions. These techniques are useful to perform exact correspondences between classical spin Hamiltonians and field-theory…
We describe a 2d analog of the Jordan-Wigner transformation which maps an arbitrary fermionic system on a 2d lattice to a lattice gauge theory while preserving the locality of the Hamiltonian. When the space is simply-connected, this…
The model which is the generalization of the one-dimensional XY-spin chain for the case of the two-dimensional square lattice is considered. The subspace of the ``string'' states is studied. The solution to the eigenvalue problem is…
We present a set of exactly solvable Ising models, with half-odd-integer spin-S on a square-type lattice including a quartic interaction term in the Hamiltonian. The particular properties of the mixed lattice, associated with mixed…
The anticommuting analysis with Grassmann variables is applied to the two-dimensional Ising model in statistical mechanics. The discussion includes the transformation of the partition function into a Gaussian fermionic integral, the…
In this paper, we show that a system of localized particles, satisfying the Fermi statistics and subject to finite-range interactions, can be exactly solved in any dimension. In fact, in this case it is always possible to find a finite…
In this paper, we first rework B. Kaufman's 1949 paper, "Crystal Statistics. II. Partition Function Evaluated by Spinor Analysis", by using representation theory. Our approach leads to a simpler and more direct way of deriving the spectrum…
Integrability conditions on local Hamiltonians for one-dimensional quantum systems to be free and interacting fermions are introduced. The definition of free fermion is the simultaneous satisfaction of the Yang-Baxter equation and Shastry's…
We apply a new anticommuting path integral technique to clarify the fermionic structure of the 2D Ising model with quenched site dilution. In the $N$-replica scheme, the model is explicitly reformulated as a theory of interacting fermions…
We define and study a long-range version of the XX model, arising as the free-fermion point of the XXZ-type Haldane--Shastry (HS) chain. It has a description via non-unitary fermions, based on the free-fermion Temperley--Lieb algebra, and…
Transfer-matrix methods, with the help of finite-size scaling and conformal invariance concepts, are used to investigate the critical behavior of two-dimensional square-lattice Ising spin-1/2 systems with first- and second-neighbor…
We discuss N=2 supersymmetric quantum mechanics on the lattice using the fermion loop formulation. In this approach the system naturally decomposes into a bosonic and fermionic sector. This allows us to deal with the sign problem arising in…
We consider the Cooper-problem on a two-dimensional, square lattice with a uniform, perpendicular magnetic field. Only rational flux fractions are considered. An extended (real-space) Hubbard model including nearest and next nearest…
We consider the spin $k/2$ XXZ model in the antiferomagnetic regime using the free field realization of the quantum affine algebra $\uqa$ of level $k$. We give a free field realization of the type II $q$-vertex operator, which describes…