Algebraic reduction of the Ising model

نویسنده

  • R. J. Baxter
چکیده

We consider the Ising model on a cylindrical lattice of L columns, with fixed-spin boundary conditions on the top and bottom rows. The spontaneous magnetization can be written in terms of partition functions on this lattice. We show how we can use the Clifford algebra of Kaufman to write these partition functions in terms of L by L determinants, and then further reduce them to m by m determinants, where m is approximately L/2. In this form the results can be compared with those of the Ising case of the superinte-grable chiral Potts model. They point to a way of calculating the spontaneous magnetization of that more general model algebraically.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Magnetic Properties and Phase Transitions in a Spin-1 Random Transverse Ising Model on Simple Cubic Lattice

Within the effective-field theory with correlations (EFT), a transverse random field spin-1 Ising model on the simple cubic (z=6) lattice is studied. The phase diagrams, the behavior of critical points, transverse magnetization,  internal energy, magnetic specific heat are obtained numerically and discussed for different values of p the concentration of the random transverse field.

متن کامل

کاهش ابعاد ماتریس انتقال در مدلهای دو بعدی آیزینگ و پاتس

 A new algebraic method is developed to reduce the size of the transfer matrix of Ising and three-state Potts ferromagnets on strips of width r sites of square and triangular lattices. This size reduction has been set up in such a way that the maximum eigenvalues of both the reduced and the original transfer matrices became exactly the same. In this method we write the original transfer matrix ...

متن کامل

On the Algebraic Complexity of Some Families of Coloured Tutte Polynomials

We investigate the coloured Tutte polynomial in Valiant’s algebraic framework of NP-completeness. Generalising the well known relationship between the Tutte polynomial and the partition function from the Ising model, we establish a reduction from the permanent to the coloured Tutte polynomial, thus showing that its evaluation is a VNP−complete problem.

متن کامل

Magnetic Properties in a Spin-1 Random Transverse Ising Model on Square Lattice

In this paper we investigate the effect of a random transverse field, distributed according to a trimodal distribution, on the phase diagram and magnetic properties of a two-dimensional lattice (square with z=4),  ferromagnetic Ising system consisting of magnetic atoms with spin-1. This study is done using the effectivefield theory (EFT) with correlations method. The equations are derived using...

متن کامل

بسط دمای بالای پذیرفتاری مدل آیزینگ شبکه کاگومه با برهم‌کنش نزدیکترین همسایه‌ها

 The Ising model is one of the simplest models describing the interacting particles. In this work, we calculate the high temperature series expansions of zero field susceptibility of ising model with ferromagnetic, antiferromagnetic and one antiferromagnetic interactions on two dimensional kagome lattice. Using the Pade´ approximation, we calculate the susceptibility of critical exponent of fer...

متن کامل

High order perturbation study of the frustrated quantum Ising chain

In this paper, using high order perturbative series expansion method, the critical exponents of the order parameter and susceptibility in transition from ferromagnetic to disordered phases for 1D quantum Ising model in transverse field, with ferromagnetic nearest neighbor and anti-ferromagnetic next to nearest neighbor interactions, are calculated. It is found that for small value of the frustr...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2008