Modified Ising model

Fig. 9.8 Modified Ising model of the SmCpii and SmCi i2 phases...

Certainly the most important models for the development of modem scaling theory of critical phenomena have been the discrete Ising model of ferromagnetism and its antipode - the continuum van der Waals model of fluid. The widespread belief is that real fluids and the lattice-gas 3D-model belong to the same universality class but the absence of any particle-hole-type symmetry in fluids requires the revised scaling EOS. The mixed variables were introduced to modify the original Widom EOS and account the possible singularity of the rectilinear diameter. 

Cluster Monte Carlo algorithms are applicable not only to the Ising model. They also work for other types of spin models. In this section and the next we consider how they can be modified to work with Potts models and... 

The calculated phase diagram for the Karaborni and Toxvaerd force field deviates significantly from the experimental observations, but the modified model gives a more quantitative description. In both cases, the shape of the coexistence curve can be fitted using the critical exponent of the three-dimensional Ising model. The two force fields yield qualitatively different structural properties. 

Basically, there are two different models that have been applied to the helix-coil transition of DNA, These models differ mainly in the treatment of a loop of broken bonds sandwiched between two helical segments. The modified Ising (MI) model considers the unwinding of the interior of a DNA molecule to take place in the same manner as the free ends. The loop entropy (LE) model accounts for a differpuce between the entropy of unbonded strands sandwiched between two helical sections and the entropy of unbonded strands at the end of the molecule. 

The modified Ising (MI) model has been applied to the DNA transition by several authors.Although the underlying model employed by these authors has been the same, the methods and approximations made have been different. The notation used in these calculations has also varied, and we will endeavor to show their connection where appropriate. Although the MI model omits the loop entropy factor, its simplicity allows an easy comparison with experiment and gives a basis for further improvements. We first obtain the melting curves of periodic DNAs and then present results for DNAs with a random distribution of A-T and G-C base pairs. 

Fig. 218. Cu(NH3)2COj. Temperature dependence of x . Magnetism fitted according to the Ising model (broken line) using J//ic= -6.2 cm, g = 2.20 and according to the modified dimer model (solid line)...

Yamashita and Miyazima [58] and Yamashita [59], [60] adopted the modified ANNNI (axial next-nearest-neighbor Ising) model with the third-neighboring interaction (ANNNI + Jj, model) and wrote the Hamiltonian... 

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