Effect of thermal bond excitations on the critical properties of covalent Ising networks

Abstract

We introduce a bond-diluted Ising model with temperature-dependent concentration of bonds, which is intended to simulate the excitations of bond degrees of freedom as in covalently bonded network liquids arising from the thermal electronic transitions between bonding and antibonding electronic states. The critical behavior of this simplified model system, called the thermalized-bond Ising model, is investigated in terms of the Monte Carlo simulation results of finite-size regular Ising systems, as input for the method of chemical potentials that is generally used to obtain the thermodynamic properties of annealed impurity models. A finite-size scaling analysis of the susceptibility and the fourth-order cumulant results in a reliable estimation of the renormalized critical exponents. The exponents are found to be consistent with the phenomenological renormalization relations, due to Fisher, despite the temperature-dependent bond dilution.

Critical behavior of the two-dimensional thermalized bond Ising model

“…where β = 1/k B T is the reciprocal temperature and k B is the Boltzmann constant [8]. We certainly do not rule out other forms of the bond concentration p. In fact, in a more realistic application one may wish to consider bonds that obey Fermi statistics, and treat the electronic occupation numbers accordingly.…”

“…(1), and δ denotes the Kronecker delta [8]. J ij = J 0 is the coupling associated with a bond, and J ij = 0 is that due to a broken bond.…”

“…Like the annealed case, and given enough time, our model system has the freedom to lower its free energy by choosing optimal arrangements of the bond variables, and to reach complete thermal equilibrium with the lattice or the structural variables. We believe that the thermalized bond Ising model [8], and the many conceivable variants thereof, can be of broader interest in the research field of phase transitions in systems with predominantly covalent bonding, such as lattice polymers and lattice protein, as they can provide for a natural bond breaking mechanism in lattice models of covalent structures. A rather similar model, known as the bond-lattice excitation model, has been introduced and studied in the context of supercooled glass-forming liquids [9].…”

“…The 3d TBIM was investigated in Ref. [8] using the method of chemical potential and the grand canonical ensemble [1]. In this paper, however, the critical behavior of 2d TBIM is investigated using the canonical ensemble Monte Carlo simulations of the model system by a suitably modified Wolff single-cluster algorithm.…”

“…In the case of the Thermalized Bond Ising Model (TBIM) each covalent bond linking a nearest neighbor pair of atoms is allowed thermally induced electronic transitions between bonding and anti-bonding electronic states [8]. Hence, it can be regarded as containing annealed bond defects with a temperaturedependent concentration.…”