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#MONTE CARLO SIMULATION TOOLS CRYSTAL BALL FUSION SERIES#
#MONTE CARLO SIMULATION TOOLS CRYSTAL BALL FUSION FREE#

Notably, near absolute zero (i.e., the critical temperature), we derive the values of the critical exponents α=0,η=-1,γ=3, and ν=1, as for the square lattice, thus proving their universal character. Closed-form expressions of the main thermodynamic functions of interest are derived in the zero-field limit. In this article we adapt a previous work concerning the two-dimensional (2D) Heisenberg classical square lattice to the case of a honeycomb lattice. High-temperature behaviors of the thermodynamic quantities are also discussed with the help of a series-expansion method. This is a visualization of a quantum-classical crossover and an evidence that the present model is a Haldane system.

#MONTE CARLO SIMULATION TOOLS CRYSTAL BALL FUSION FREE#

The edge contribution in the open-chain susceptibility is attributed to the two S=1 effective spins localized at the chain ends at low temperatures, while to an S=2 free spin at high temperatures. As temperature goes to zero, the magnetic susceptibility vanishes for the periodic chains, while it diverges for the open chains. The specific heat shows a well-pronounced Schottky anomaly but the maximum is located at a temperature much larger than the Haldane gap of the system.

Temperature and size dependences of the energy, the specific heat, and the magnetic susceptibility are calculated and edge effects on them are investigated in detail. Thermodynamic properties of S=2 antiferromagnetic Heisenberg chains are studied not only under the periodic boundary condition but also under the open one employing a quantum Monte Carlo method. Finally, the al are employed to discuss two questions of current interest: (1) Does the critical exponent gamma-in the assumed form of the divergence of chi, chi~(T-Tc)-gamma as T->Tc+-have the value 43 for the fcc, bcc, and sc lattices? (2) Do high-temperature expansions suggest a phase transition (Tc!=0) for some two-dimensional lattices with nearest-neighbor ferromagnetic interactions? It is argued that extrapolation suggests gamma is definitely greater than 43 for the fcc, bcc, and sc lattices, and that Tc is appreciably different from zero for the plane square and triangular lattices. The general lattice expressions are then used to evaluate these al numerically for three two-dimensional lattices and for three cubic lattices.

#MONTE CARLO SIMULATION TOOLS CRYSTAL BALL FUSION SERIES#

The first nine terms al for loose-packed lattices and the first seven terms for close-packed lattices in the susceptibility series are explicitly obtained in terms of Domb's 'general lattice constants' plx. The high-temperature series expansion of the zero-field magnetic susceptibility, chichiCurie=1+l=1∞al(JkT)l, is related to the diagrammatic representation of the corresponding high-temperature expansion of the zero-field static spin correlation function beta presented elsewhere. Single crystal hysteresis loops in magnetisation versus external magnetic field measurements show the temperature and sweep rate dependence indicative of single-molecule magnetism behaviour. For 5 however, these stabilise an S=11/2 spin ground state with an axial zero-field splitting parameter of D=−0.46cm−1. Magnetic studies reveal the presence of dominant antiferromagnetic interactions between the Fe centres in all eight complexes which results in the presence of small spin ground states for complexes 1–4 and 6–8. These include the rhomb or diamond-like clusters (1, R=Me, R′=Et 2, R=Ph, R′=Me 3, R=CMe3, R′=Me) the related nonanuclear and undecanuclear clusters (4) and (5) (dmhp=4,6-dimethyl-2-hydroxypyrimidine) and the octametallic and hexadecametallic wheels (6, R=Ph 7, R=CMe3) and (NO3)4 (8). Reaction of the tripodal ligand 1,1,1-tris(hydroxymethyl)ethane (H3thme) with a variety of Fe(III) precursors under both ambient and solvothermal conditions has led to the isolation of a number of new complexes ranging in nuclearity from 4 to 16.

Monte carlo simulation tools crystal ball fusion