148
I. Gudyma and A. Maksymov
spin states, we have investigated the dependence of the temperature transition point
on the strength of fluctuations that for small systems and open boundaries becomes
very relevant.
We apply the next Metropolis algorithm to find the temperature transition curves
that are the main characteristic of the system: (i) fix the value of temperature; (ii) fix
initial spin configuration; (iii) find the energy for initial spin configuration; (iv) flip
arbitrarily one spin from the lattice; (v) calculate the energy of new spin configuration;
(vi) evaluate the transition probability for new configuration and decide if transition
is possible or not; and (vii) if the transition is possible the system magnetization
(and other necessary parameters) may be found; otherwise, the spin configuration
remains unchanged and the next Monte Carlo step starts by repeating the algorithm
from step (i). The spin transition probability on step (vi) for arbitrary chosen spin s i
is given by the following expression:
P(s i → −s i ) = min
1, exp
−
ΔH {s i }
kT
,
(7)
where ΔH {s i } is the energy difference when a spin changes between s i and −s i :
ΔH {s i } = 2J s i
j
s j − 2h i s i .
(8)
For provided simulations, the Boltzmann constant is fixed at k = 1.
We start the calculations of transition curves from high temperature that corresponds to HS state where all spins are “up.” The thermal cycle is considered finished
if a temperature sweep from the HS state to the LS one, where all spins are “down,”
and back to initial HS state takes place. The final system’s magnetization is calculated
at every temperature value by averaging over an ensemble of pseudospin values s i
taken from the stationary regime of MC trajectory. The magnetization m = =s i of
Ising model and the order parameter of spin-crossover system, i.e., the HS fraction
n H S , are related by the following expression:
n H S =
m + 1
2
.
(9)
The temperature at which the fraction of HS and LS molecules is the same, i.e., n H S =
0.5, during cooling and heating of spin-crossover system is defined as transition
temperature.
4 Cooperative Behavior in 3D Spin-Crossover Ising-Like
Model with Correlated Fluctuations
We have studied the thermal phase transition and the bistable behavior of 3D Isinglike spin-crossover system (3) for external random field with various statistical prop-
I. Gudyma and A. Maksymov
spin states, we have investigated the dependence of the temperature transition point
on the strength of fluctuations that for small systems and open boundaries becomes
very relevant.
We apply the next Metropolis algorithm to find the temperature transition curves
that are the main characteristic of the system: (i) fix the value of temperature; (ii) fix
initial spin configuration; (iii) find the energy for initial spin configuration; (iv) flip
arbitrarily one spin from the lattice; (v) calculate the energy of new spin configuration;
(vi) evaluate the transition probability for new configuration and decide if transition
is possible or not; and (vii) if the transition is possible the system magnetization
(and other necessary parameters) may be found; otherwise, the spin configuration
remains unchanged and the next Monte Carlo step starts by repeating the algorithm
from step (i). The spin transition probability on step (vi) for arbitrary chosen spin s i
is given by the following expression:
P(s i → −s i ) = min
1, exp
−
ΔH {s i }
kT
,
(7)
where ΔH {s i } is the energy difference when a spin changes between s i and −s i :
ΔH {s i } = 2J s i
j
s j − 2h i s i .
(8)
For provided simulations, the Boltzmann constant is fixed at k = 1.
We start the calculations of transition curves from high temperature that corresponds to HS state where all spins are “up.” The thermal cycle is considered finished
if a temperature sweep from the HS state to the LS one, where all spins are “down,”
and back to initial HS state takes place. The final system’s magnetization is calculated
at every temperature value by averaging over an ensemble of pseudospin values s i
taken from the stationary regime of MC trajectory. The magnetization m = =s i of
Ising model and the order parameter of spin-crossover system, i.e., the HS fraction
n H S , are related by the following expression:
n H S =
m + 1
2
.
(9)
The temperature at which the fraction of HS and LS molecules is the same, i.e., n H S =
0.5, during cooling and heating of spin-crossover system is defined as transition
temperature.
4 Cooperative Behavior in 3D Spin-Crossover Ising-Like
Model with Correlated Fluctuations
We have studied the thermal phase transition and the bistable behavior of 3D Isinglike spin-crossover system (3) for external random field with various statistical prop-