Frustrated spin systems

In conclusion we note that the construction of considered models is based on the following property. Their Hamiltonians are the sums of the cell Hamiltonians that are local and non-commuting with each other. At the same time the ground-state wave function of the total Hamiltonian is the ground state for each cell Hamiltonian. It is clear that these models are rather special. Nevertheless, the study of them is useful for understanding properties of the real frustrated spin systems and strongly correlated electronic models. 

So far, we have discussed quantum Monte Carlo approaches to quantum phase transitions in boson and spin systems. In these systems, the statistical weight in the Monte Carlo procedure is generally positive definite, so there is no sign problem. Note that for spin systems, this is only true if there is no frustration. Frustrated spin systems in general do have a sign problem. 

It is probably fair to say that Monte Carlo simulations of model systems that are free of the sign problem (bosons, spin systems without frustration, and some special fermionic systems) have become so powerful that the properties of their quantum phase transitions can be determined quantitatively with high precision (see, e.g., the accuracy of some of the exponent values quoted in the preceding sections). For many frustrated spin systems, in contrast, the results are limited to a qualitative level, and for quantum phase transitions in generic fermionic systems (with sign problem), direct computational attacks are still of limited utility. 

At low temperatures, frustrated spin systems are easily deformed by disturbances which spht degenerate ground states by changing the magnetic interactions. If the disturbance has long-range character, deformation will be cooperative... 

The frustration effects are implicit in many physical systems, as different as spin glass magnets, adsorbed monomolecular films and liquid crystals [32, 54, 55], In the case of polar mesogens the dipolar frustrations may be modelled by a spin system on a triangular lattice (Fig, 5), The corresponding Hamiltonian consists of a two particle dipolar potential that has competing parallel dipole and antiparallel dipole interactions [321, The system is analyzed in terms of dimers and trimers of dipoles. When the dipolar forces between two of them cancel, the third dipole experiences no overall interaction. It is free to permeate out of the layer, thus frustrating smectic order. 

Radicals have been known for many years to form organic paramagnetic materials with numerous magnetic properties (ferro- or ferri-magnetism, spin Peierls transition, spin frustration, spin ladder systems) (see [51-60] for verdazyl radicals, [61-68] for thiazyl radicals, [69] for nitronyl nitroxide and [70-78] for Tempo radicals) (Fig. 6). When they are in their cationic form, they are valuable candidates for an association with the M(dmit)2 systems they will then provide the magnetic properties thanks to their free electron(s), whereas the M(dmit)2 moieties will provide the electrical properties. 

Shimizu Y, Kurosaki Y, Miyagawa K, Kanoda K, Maesato M, Saito G (2005) NMR study of the spin-liquid state and Mott transition in the spin-frustrated organic system, k-(ET)2Cu2(CN)3. Synth Met 152 393-396... 

A different approach simulates the thermodynamic parameters of a finite spin system by using Monte Carlo statistics. Both classical spin and quantum spin systems of very large dimension can be simulated, and Monte Carlo many-body simulations are especially suited to fit a spin ensemble with defined interaction energies to match experimental data. In the case of classical spins, the simulations involve solving the equations of motion governing the orientations of the individual unit vectors, coupled to a heat reservoir, that take the form of coupled deterministic nonlinear differential equations.23 Quantum Monte Carlo involves the direct representation of many-body effects in a wavefunction. Note that quantum Monte Carlo simulations are inherently limited in that spin-frustrated systems can only be described at high temperatures.24... 

Exact ground states of one- and two-dimensional frustrated quantum spin systems... 

Vibronic Interaction in a Spin-Frustrated Triangular System... 

There exists a maximum pressure beyond which the smectic A phase disappears (see Fig. Id). The p(7 )-phase boundary nematic-smectic A has an elliptic shape. Reentrant behavior has been found for many systems, and therefore several theoretical treatments have been considered to explain this phenomenon. The most successful is probably the frustrated spin-gas model, which also predicts the sensitivity to the number of carbon atoms in the alkyl chain of the molecule. ... 

Antiferromagnetism on a triangular net is one of the problems of recent interest in the physics of spin systems. The main point is the frustration, i.e., existence of infinitely degenerate ground states. A typical example is CsCoClj (Mekata 1977, Mekata et al. 1986). 

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