Heisenberg magnet

Consider the site-diluted square lattice Heisenberg model given by the Hamiltonian 

Sandvik performed quantum Monte Carlo simulations of the Heisenberg Hamiltonian on the critical infinite percolation cluster (p = pp) using the stochastic series expansion method with operator loop update. 

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The uniform Heisenberg magnetic chain has been an object of study for three quarters of a century, dating back to the initial work of Bethe. Unhke the equivalent Ising and XY-chains, the Heisenberg model cannot be solved analytically. The first calculations of the susceptibihty and specific heat... 

Fig. 49. Schematic phase diagrams predicted for the antiferromagnetic order at the surfaces of isotropic Heisenberg magnets (n = 3, upper part) and of XY magnets (n = 2), lower part. Phases occurring are bulk paramagnetic (BP), bulk ferromagnetic (BP), surface paramagnetic (A P), surface ferromagnetic (A P), surface antifcrromagnctic (SAF) and surface spin flop (iSSF). From Binder and Landau (1985).

We will use our first example, the spin- quantum Heisenberg magnet, to further illustrate the world-line quantum Monte Carlo method. The model we present is the quantum XXZ model ... 

Since the Eu chalcogenides are considered to be models for Heisenberg magnets, the isotropic exchange hamiltonian... 

The experimental critical exponents of table 19.3 can now be compared with the predictions for 3 dimensional Heisenberg magnets. While the general agreement between theory and experiment is quite good, the exponent y of EuS is an exception, approaching nearly the molecular field value. As pointed out by Berkner (1975) there is a general trend for low Tc materials to exhibit smaller y values than theory predicts. On the other hand this is a clear indication that the... 

Polymetallic systems are magnetically coupled. The magnetic coupling in the simple Heisenberg model can be described by the following Hamiltonian (38-40) ... 

Temperature dependence of magnetic susceptibility of the PF6 salt was measured from 300 to 4 K at 5 T [35], The spin susceptibility of this salt gradually decreases from 300 to 50 K. Below 50 K, the susceptibility exhibits a rapid decrease accompanied by anisotropic temperature dependence, which is an indication of the long-range antiferromagnetic ordering. A one-dimensional Heisenberg model is... 

Much attention has been paid to Monte Carlo simulations of magnetic ordering, and its variation with temperature. Such models assume a particular form for the magnetic interactions, e.g. the Ising or Heisenberg Hamiltonian (see e.g. Binder... 

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