Monte Carlo Simulations, Renormalization Group Theory

1 Monte Carlo Simulations, Renormalization Group Theory 

However, the dimension g of the Heisenberg Hamiltonian grows rapidly with the number of magnetic sites N and the spin moment of these sites. For a model with all spin moments equal to 5 = the dimension is given by (Table 3.2) 

2 (( 5+1/2) ) and for lattices with S = 1 spin moments the dimension is given by 

Renormalization Group theory The partition function Q is the central quantity of statistical mechanics and many thermodynamic functions can be derived from it. The partition function of the one-dimensional Ising chain is 

we have shown that the partition function of the whole system can be written in terms of properties that only depend on half the number of centers 

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The finite temperature studies of Lennard-Jones lattice gas systems have been performed for the square [105,116], rectangular [106] and triangular [100,111,112] lattices using different approaches, including the simple mean-field theory, the renormalization group method, Monte Carlo simulation and Monte Carlo version of the coherent anomaly method. 

The same group also investigated the case of ring diblock copolymers in a common 0 solvent, a good solvent, and in selective solvents, using theoretical (renormalization group theory) and numerical simulation (Monte Carlo) methods [288]. In this way the average dimensions of each block and of the whole molecule were obtained and compared with results on linear diblock copolymers. 

Figure 9 Dimensionless apparent molecular weight Mapp times the concentration c of giant surfactant micelles of hexadecyl trimethyl ammonium bromide in brine, obtained by means of light scattering measurements at a temperature of 306 K. Circles experimental data of Buhler and coworkers [50]. Line renormalization group theory for self-assembled flexible chains fitted to the data [51,52], Also indicated by the dashed lines are the predictions of scaling theory in the dilute and semidilute regimes [1,53], which agree well with results of Monte Carlo simulation [52],...

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