Heisenberg spin system

Fig. 304. CuSe03 2H20. Temperature dependence of 1/Xn,. Curve fitted for a linear Heisenberg spin system with J/k = -33K,g = 2.00[73A15].

The pure RKKY interaction is isotropic, and the canonical spin glass systems are therefore often referred to as Heisenberg spin glasses. However, some anisotropy is also present in those systems originating from dipolar interaction and interaction of the Dzyaloshinsky-Moriya (DM) type [73]. The latter is due to spin-orbit scattering of the conduction electrons by non-magnetic impurities and reads... 

In present-day quantum chemistry the Heisenberg Spin Hamiltonian is widely applied for the description of magnetic coupling in transition-metal clusters and may read in the case of a many-electron system,... 

S2 possesses the eigenvalues S(S + 1). For a spin-1/2 dimer (S can be 0 or 1), the same values are obtained from the derivation of the Bleaney-Bowers equation. For spin systems in an external magnetic field, the Zeeman operator Hmag = -g/ BB S accounts for Zeeman splitting. The isotropic Heisenberg Hamiltonian for multiple spin centers can be expanded by adding the individual coupling pairs ... 

Key words ESR, EPR, Heisenberg chain, Haldane, spin-Peierls, large-D, low-dimensional spin systems... 

For organic spin systems, one frequently assumes applicability of Heisenberg spin behavior, in which all interactions can be reasonably modeled by pairwise exchange interactions. A typical Heisenberg spin Hamiltonian for exchange Jy between various spin sites i and j, with spin quantum numbers S, and Sj, is given in the following equation ... 

In addition, the electron spin system also exhibits an exchange energy, often called the Heisenberg exchange, denoted by Ja °r Sl opSl where J0 represents a coulombic repulsion term (Ref. 7, Section 6.2.1) not to be confused with the primary angular momentum quantum number /. In general, the scalar Ja can be anisotropic, that is generated via a 3 x 3 matrix. 

The lattice dimensionality of the interacting spin system describes the number of directions in which there are extended interaction pathways. Along with the spin dimensionality, the lattice dimensionality determines if a magnetic system can spontaneously undergo a transition to a magnetically ordered state at a finite temperature (see Section 2.6). Spin and lattice dimensionalities are independent parameters so within each class of lattice dimensionality, the spins can be described by Ising-like, XY-like, or Heisenberg Hamiltonians. 

In this section we will generalize the Monte Carlo methods described in section 2 for classical spin systems to quantum spin systems. As an example we will use the spin-1/2 quantum Heisenberg o XXZ models with Hamiltonian... 

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