H Nakanishi and H E Stanley 1981 J. Phys. A: Math. Gen. 14 693 doi:10.1088/0305-4470/14/3/017
H Nakanishi and H E Stanley
Show affiliationsCluster statistics obtained by the Monte Carlo method for percolation processes in systems of dimensionality two to seven are analysed for the percolation analogue of the thermodynamic equation of state. In particular, the authors calculate the scaling functions for the analogues of the thermodynamic potentials and their derivatives, and investigate their dependence on dimension d. They are guided by the two exactly soluble limits of d=1 and the Bethe lattice (d= infinity ). The scaling region, where a good degree of data collapsing can be observed, is investigated in terms of the two 'thermodynamic' variables, one of which is analogous to the temperature and the other to the magnetic field. The characteristic forms of the scaling functions are closely related to the 'thermodynamic' stability conditions.
05.70.Ce Thermodynamic functions and equations of state
64.60.A- Specific approaches applied to studies of phase transitions
82B80 Numerical methods (Monte Carlo, series resummation, etc.) (See also 65-XX, 81T80)
82B30 Statistical thermodynamics (See also 80-XX)
82B26 Phase transitions (general)
82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs
Condensed matter: electrical, magnetic and optical
Issue 3 (1 March 1981)
H Nakanishi and H E Stanley 1981 J. Phys. A: Math. Gen. 14 693
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