HEAT CAPACITY CRITICAL EXPONENT IN THE BOND PROBLEM FOR ONE-DIMENSIONAL PERCOLATION MODEL TAKING INTO ACCOUNT THE EXTERNAL FIELD

T.V. Yakunina, V.N. Udodov
DOI: 10.25699/SSSB.2020.29.56918 Download PDF
Abstract: A one-dimensional percolation model is constructed for the bond problem for percolation along not nearest neighbors. New algorithms are proposed for finding the percolation threshold for gratings of arbitrary size with an arbitrary percolation radius without constructing a covering lattice and an adjacency matrix. These algorithms work on computers much faster than the known ones. The threshold is calculated for a percolation radius of up to eight. In addition, the free energy and critical heat capacity exponent were calculated for chains of various lengths up to a percolation radius of six. The influence of a weak field is taken into account in the work. The results may find application in simulating the hopping conductivity of semiconductors at low temperatures.
Index terms: computer modeling, percolation theory, one-dimensional bond problem, percolation threshold, free energy, the critical exponent of the specific heat.

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