By H T Diep
Pissed off spin platforms were first investigated 5 a long time in the past. famous examples comprise the Ising version at the antiferromagnetic triangular lattice studied through G H Wannier in 1950 and the Heisenberg helical constitution came across independently through A Yoshimori, J Villain and T A Kaplan in 1959. despite the fact that, many houses of annoyed platforms are nonetheless now not good understood at the moment. contemporary stories show that tested theories, numerical simulations in addition to experimental thoughts have encountered many problems in facing pissed off platforms. This quantity highlights the most recent theoretical, numerical and experimental advancements within the box. The e-book is meant for post-graduate scholars in addition to researchers in statistical physics, magnetism, fabrics technological know-how and diverse domain names the place genuine platforms could be defined with the spin language. particular demonstrations of formulae and entire arguments resulting in very important effects are given.
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Extra info for Frustrated Spin Systems
The three kinds of partially disordered phases and the ferromagnetic phase are denoted by I, II , III and F, respectively. be shown below, we find a new and richer behavior of the phase diagram: in particular, the reentrance region is found to be extended to infinity, unlike systems previously studied, and for some given set of interactions, there exist two disorder lines which divide the paramagnetic phase into regions of different kinds of fluctuations with a reentrant behavior. Following the method exposed in section 3, one obtains a checkerboard Ising model with multispin interactions.
2. The 32-vertex model The 32-vertex model is defined by a triangular lattice of N points, connected by edges between neighboring sites. These edges can assume two states, symbolized by an arrow pointing in or pointing out of a site. In the general case, there are 64 allowed vertex configurations. If only an odd number of arrows pointing into a site are allowed, we have 32 possible vertex configurations. This is the constraint that characterizes the 32-vertex model. ,32)) and a corresponding vertex weight, defined as it is shown in Fig.
22a) between the partially disordered (PD) phase of type III (see Fig. 21) and the ferromagnetic (F) 34 H. T. Diep and H. Giacomini phase with an endpoint at j3 = — 1. i] decreases with decreasing a , from (3\ = 0 for a at infinity to Pi = — 1 for a = 0 (zero width). Note that as a decreases, the PD phase III is depressed and disappears at a = 0, leaving only the F phase (one critical line, see Fig. 22b). The absence of order at zero a for (3 smaller than -1 results from the fact that in the ground state, this region of parameters corresponds to a superdegenerate line separating the two PD phases II and III (see Fig.