The Two-Dimensional Infinite Heisenberg Classical Square Lattice: Zero-Field Partition Function and Correlation Length
نویسندگان
چکیده
The nonlinear σ-model has known a new interest for it allows to describe the properties of two-dimensional quantum antiferromagnets which, when properly doped, become superconductors up critical temperature notably high compared other types superconducting materials. This model been conjectured be equivalent at low temperatures Heisenberg model. In this article we rigorously examine 2d-square lattices composed classical spins isotropically coupled between first-nearest neighbors (i.e., showing couplings). A general expression characteristic polynomial associated with zero-field partition function is established any lattice size. infinite-lattice limit numerical study select dominant term: written as l-series eigenvalues, each one being characterized by unique index l whose origin explained. Surprisingly shows very simple exact closed-form valid temperature. thermal basic l-term point out crossovers l- and (l+1)-terms. Coming from where l=0-term going zero Kelvin, l-eigen¬values increasing l-values are more selected. At absolute becomes infinite all successive l-eigenvalues equivalent. As z-spin correlation null positive but equal unity (in value) zero. Using an analytical method similar employed also give spin-spin correlations well length. zero-temperature obtain diagram magnetic phases which derived through renormalization approach. By taking low-temperature length same expressions corresponding ones renor¬malization process, zone phase diagram, thus bringing first time strong validation full solution
منابع مشابه
Exact low-temperature series expansion for the partition function of the zero-field Ising model on the infinite square lattice
In this paper, we provide the exact expression for the coefficients in the low-temperature series expansion of the partition function of the two-dimensional Ising model on the infinite square lattice. This is equivalent to exact determination of the number of spin configurations at a given energy. With these coefficients, we show that the ferromagnetic-to-paramagnetic phase transition in the sq...
متن کاملPartition function zeros of the square lattice Potts model.
We have evaluated numerically the zeros of the partition function of the q-state Potts model on the square lattice with reduced interactions K . On the basis of our numerical results, we conjecture that, both for finite planar self-dual lattices and for lattices with free or periodic boundary conditions in the thermodynamic limit, the zeros in the Resxd . 0 region of the complex x seK 2 1dypq...
متن کاملPair-correlation function in two-dimensional lattice gases.
The pair-correlation function in two-dimensional lattice gases is computed by means of three discretized classical equations for the structure of liquids: the hypernetted-chain, the Percus-Yevick, and the crossover integral equations. The equations are numerically solved by an iteration procedure. Two different systems are considered: the Ising-Peierls lattice gas with nearest-neighbor interact...
متن کاملDuality and even number spin-correlation functions in the Two dimensional square lattice Ising model
The Kramers-Wannier duality is shown to hold for all the even number spin correlation functions of the two dimensional square lattice Ising model in the sense that the high temperature (T > Tc) expressions for these correlation functions are transformed into the low temperature (T < Tc) expressions under this duality transformation. PACS: 05.70.Jk The two dimensional Ising model remains one of ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: American Journal of Theoretical and Applied Statistics
سال: 2021
ISSN: ['2326-9006', '2326-8999']
DOI: https://doi.org/10.11648/j.ajtas.20211001.16