Spin-glass Hamiltonian

As mentioned above, Hopfield s original approach to this problem was to introduce an energy function reminiscent of a spin-glass Hamiltonian ... 

Ogata et al. attacked the same nucleic acid conformation problem, but replaced the buildup scheme of Lucasius with a local filter that is equivalent to the use of a rotamer library. In both cases, these methods must deal with the fact that this is an underconstrained problem because several of the dihedrals have no NOEs associated with them. Schuster earlier treated a simple model of RNA to predict three-dimensional (3D) conformations, using a variant on a spin-glass Hamiltonian as his fitness function. The simple model used allowed for the analysis of the complexity of the fitness landscape, couched in terms of the genotype-to-phenotype mapping. 

This analogy was recently exploited by P. Tarazona" to solve the quasi-species model for several choices of the fitness landscape A(S). Since the properties which affect the reproducing efficiency of RNA molecules in experiments are rather complex, it is costumary to represent A(S) by a random function, such as a spin-glass Hamiltonian. The simplest choice is to assume that A(S) takes on independent, identically distributed, random values for each different genotype S. This corresponds to identify the fitness landscape with the Random Energy Model of spin-glasses introduced by B. Derrida. ... 

Much of what is currently known about spin glasses can be traced back to the pioneering work of Edwards and Anderson [edw75]. Their idea was to try to capture the essential properties of real spin glasses with a simple Jsiug-like Hamiltonian of the form ... 

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. 

The Hamiltonian of an Ising spin glass, given by Edwards and Anderson (EA) [78], is... 

Recent zero-field studies of the free in longitudinal fields have revealed new and unique information on spin glass and other systems but here we concentrate on muonium and muonium-like states in zero magnetic field. In this case, precession is not observed in the classical sense of the word but rather a modulation of the muon polarization with time. This can be most easily understood in the case of muonium itself in terms of the isotropic Hamiltonian of Equation 30. As noted above, muonium is formed via the "capture" of an electron from the stopping medium. Since the fi is longitudinally polarizedl"3 (a ) but the captured e" is not (Qg or Pq), muonium forms initially in two spin states, defined by A> = lV°e> = I 1 1> and B> = I o /3e> = 1//2 10> +... 

The spectrum of the low-spin manganese(n) complex, [Mn(dppe)2(CO)(CN-Bu)]2+, (dppe = Ph2PCH2CH2PPh2), in a CH2C12/THF glass is shown in Figure 4.4(a).24 The spin Hamiltonian parameters, obtained from least-squares... 

In previous chapters we have seen that the Hamiltonian describing a nuclear spin system is considerably simplified when molecules tumble rapidly and randomly, as in the liquid state. However, that simplicity masks some fundamental properties of spins that help us to understand their behavior and that can be applied to problems of chemical interest. We turn now to the solid state, where these properties often dominate the appearance of the spectra. Our treatment is limited to substances such as molecular crystals, polymers, and glasses, that is, solids in which there are well-defined individual molecules. We do not treat metals, ionic crystals, semiconductors, superconductors, or other systems in which delocalization of electrons is of critical importance. 

O- and S-Donor Ligands. In frozen aqueous glass, [Ti(H20)6] has an axial spin Hamiltonian with = 1.988 + 0.002, and g = 1.892 0.002. The stability constant of TiCP in aqueous HCl for p = 0 is loge Kq = 1.27—1.28 in good agreement with values obtained for CrCP and FeCP The stability constant of TiSO has also been determined. ... 

In the limit of a weak external field the model Hamiltonian describes the well-known Kubo-Anderson random frequency modulation process whose properties are specified by statistics of Aco -(t) [58-60]. When the fluctuating part of the optical frequency Am - is a two-state random telegraph process, the Hamiltonian describes a SM (or spin of type A) coupled to J bath molecules (or spins of type B), these being two-level systems. Under certain conditions, this Hamiltonian describes a SM interacting with many two-level systems in low-temperature glasses that has been used to analyze SM line shapes [14-16, 63, 65, 66]. 

The splitting of energy levels is similar to that described for 3d . In all single crystals and glasses studied, the complexes show axial symmetry. Thus the spin Hamiltonian Eq. (8) is used. 

Mn(II) EPR spectra in biological systems are very much like those in glasses — e.g., that in lithium-borate glass (Griscom Griscom, 1967) matches closely that in kinase oxalate ternary complex (Reed Markham, 1984 referred to hereafter as RM, and references therein). Table 1 lists the measured values of the spin-Hamiltonian parameters parameters (g, D, E) in some proteins, as taken from RM. 

Simulation of EPR spectra in glasses requires use of rather precise Mn(II) EPR lineshapes taking into account distribution of spin-Hamiltonian parameters [5], Only the parameter values restricted to Z) gllaS, gldsS, a will here be considered. The resonance magnetic fields for transitions between states M, m and M-1, m+i, denoted by... 

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