Fifty Years of the Exact solution of the Two-dimensional Ising Model by Onsager

نویسندگان

  • Somendra M. Bhattacharjee
  • Avinash Khare
چکیده

The exact solution of the two-dimensional Ising model by Onsager in 1944 represents one of the landmarks in theoretical physics. On the occassion of the fifty years of the exact solution, we give a historical review of this model. After briefly discussing the exact solution by Onsager, we point out some of the recent developments in this field. The exact solution by Onsager has inspired several developments in various other fields. Some of these are also briefly mentioned.

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 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

The critical temperature of two-dimensional and three-dimensional Ising models

The critical temperatures of the Ising model can be obtained by considering the elementary cells of the corresponding lattice, namely the square lattice in two dimensions and the cube in three dimensions. The configurations in the statistical sum of a cell are divided into nondegenerate and degenerate cases. At the critical temperature of the infinite lattice the contributions of these two grou...

متن کامل

Numerical evaluations of the critical properties of the two - dimensional Ising modeP

Scaling transformations are used in numerical calculations of the properties of the two4imensional Ising model near its critical point. When compared with the exact Onsager solution, the best approximation is seen to lead to 1 part in 10 accuracy for the two largest scaling indices. This rather accurate calculation is obtained by utilizing a scaling transformation which depends upon a parameter...

متن کامل

Basic statistical models

1 Definition and the basic properties The Ising model (IM) was invented by Lenz. His student Ising has found the partition function of the 1d model and tried to solve 2d model but failed. The exact solution of 2d model was found by Onsager in 1942-1944. It is one of the fundamental results in statistical physics. The IM consist of spins σ x = ±1 ascribed to sites of a lattice x. The energy of ...

متن کامل

MATH 505 Project: Ising model – Phase transition

Ising model is a mathematical model of ferromagnetism in statistical mechanics, which was invented by Wilhelm Lenz (1920). Wilhelm Lenz gave the model as a problem to his student Ernst Ising. Ising solved this problem in one-dimension in his PHD thesis (1924)[1], which worked on linear chains of coupled magnetic moments. Rudolf Peierls named this model by Ising model in his 1936 publication “On...

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 2005