150
I. Gudyma and A. Maksymov
squares is calculated for the case without fluctuations. The spin–spin interaction J
was chosen in order to have the pronounced hysteresis. The hysteresis loops marked
by circles, triangles up, and triangles down correspond to intensities of white fluctuations ε = 100, ε = 250, and ε = 450 accordingly, which are uncorrelated in space
and time (white fluctuations) and are described by statistical conditions (4). As one
can see from Fig. 2a, the white uncorrelated fluctuations have destructive impact on
system’s cooperativity, and for intensity ε = 450 the hysteresis disappears. The similar behavior can be seen for the case of colored in time fluctuations (uncorrelated
in space), given by statistical conditions (5), which is displayed in Fig. 2b where
the hysteresis loops are calculated for intensities ε c = 100 (squared line), ε c = 450
(circled red line), and ε c = 1200 (triangled up green line). In this case, the system
cooperativity is less sensitive to the fluctuations which is clearly seen from the comparison of loops for intensities ε = ε c = 450. At this intensity, the width of hysteresis
slightly changes for the system with colored fluctuations in comparison to fluctuationless case, whereas for the uncorrelated (white) fluctuations at this intensity the
hysteresis vanishes. For the system with correlated fluctuations, the collapse of hysteresis width takes place at much higher intensity of fluctuations. For studied system,
the hysteresis disappears at ε c = 1200 that is higher than the energy gap between LS
and HS states.
The impact of autocorrelation time τ that describes the correlations degree of
colored fluctuations on hysteresis loop is shown in Fig. 2c. The curves marked by
red circles, black squares, green triangles up, cyan diamonds, and blue triangles down
are calculated for values of autocorrelation time τ = 2, τ = 4, τ = 8, τ = 25, and
τ = 50, respectively. For this case, we keep the fluctuation intensity at ε c = 450 that
in the limit of τ → 0 corresponds to white fluctuations and therefore provides the
collapse of hysteresis (see Fig. 2a). With increase of degree of autocorrelation τ , one
can see the nonlinear enlargement of hysteresis loop (the hysteresis widths in Fig. 2c
slightly change for τ = 8; 25; 50 in comparison to ones for τ = 2; 4; 8).
If a spin–spin interaction J is lower than threshold one between non-hysteresis
and hysteresis behavior, a gradual phase transition is predicted. Nonetheless, the
fluctuations of crystal field effectually change the behavior of the spin-crossover
system. The characteristic transition curves for threshold interaction J = 55 are
presented in Fig. 2d for deterministic system and for the system with the fluctuating
fields that are assumed to be a white Gaussian and colored stochastic processes. In
this case, the squared line corresponds to the deterministic system, the circled and
triangled up lines are for the system with white fluctuations with intensities ε = 20
and ε = 140, respectively, and the lines indicated by triangles down and diamonds
describe the system with time-correlated fluctuations with intensity ε c = 140 and
different degrees of correlations τ = 5 and τ = 50, respectively.
The peculiar feature of temperature curves for the system located on the boundary
between non-hysteretic and hysteretic phase space regions is a hysteresis induced
by fluctuations that appears at small fluctuation strength and vanishes with increase
of their intensity. As one can observe from Fig. 2d, the system shows hysteretic
properties in case of relatively small intensity of white fluctuations (ε = 20) which
collapses with further increase in fluctuation strength. In studied case, the threshold
I. Gudyma and A. Maksymov
squares is calculated for the case without fluctuations. The spin–spin interaction J
was chosen in order to have the pronounced hysteresis. The hysteresis loops marked
by circles, triangles up, and triangles down correspond to intensities of white fluctuations ε = 100, ε = 250, and ε = 450 accordingly, which are uncorrelated in space
and time (white fluctuations) and are described by statistical conditions (4). As one
can see from Fig. 2a, the white uncorrelated fluctuations have destructive impact on
system’s cooperativity, and for intensity ε = 450 the hysteresis disappears. The similar behavior can be seen for the case of colored in time fluctuations (uncorrelated
in space), given by statistical conditions (5), which is displayed in Fig. 2b where
the hysteresis loops are calculated for intensities ε c = 100 (squared line), ε c = 450
(circled red line), and ε c = 1200 (triangled up green line). In this case, the system
cooperativity is less sensitive to the fluctuations which is clearly seen from the comparison of loops for intensities ε = ε c = 450. At this intensity, the width of hysteresis
slightly changes for the system with colored fluctuations in comparison to fluctuationless case, whereas for the uncorrelated (white) fluctuations at this intensity the
hysteresis vanishes. For the system with correlated fluctuations, the collapse of hysteresis width takes place at much higher intensity of fluctuations. For studied system,
the hysteresis disappears at ε c = 1200 that is higher than the energy gap between LS
and HS states.
The impact of autocorrelation time τ that describes the correlations degree of
colored fluctuations on hysteresis loop is shown in Fig. 2c. The curves marked by
red circles, black squares, green triangles up, cyan diamonds, and blue triangles down
are calculated for values of autocorrelation time τ = 2, τ = 4, τ = 8, τ = 25, and
τ = 50, respectively. For this case, we keep the fluctuation intensity at ε c = 450 that
in the limit of τ → 0 corresponds to white fluctuations and therefore provides the
collapse of hysteresis (see Fig. 2a). With increase of degree of autocorrelation τ , one
can see the nonlinear enlargement of hysteresis loop (the hysteresis widths in Fig. 2c
slightly change for τ = 8; 25; 50 in comparison to ones for τ = 2; 4; 8).
If a spin–spin interaction J is lower than threshold one between non-hysteresis
and hysteresis behavior, a gradual phase transition is predicted. Nonetheless, the
fluctuations of crystal field effectually change the behavior of the spin-crossover
system. The characteristic transition curves for threshold interaction J = 55 are
presented in Fig. 2d for deterministic system and for the system with the fluctuating
fields that are assumed to be a white Gaussian and colored stochastic processes. In
this case, the squared line corresponds to the deterministic system, the circled and
triangled up lines are for the system with white fluctuations with intensities ε = 20
and ε = 140, respectively, and the lines indicated by triangles down and diamonds
describe the system with time-correlated fluctuations with intensity ε c = 140 and
different degrees of correlations τ = 5 and τ = 50, respectively.
The peculiar feature of temperature curves for the system located on the boundary
between non-hysteretic and hysteretic phase space regions is a hysteresis induced
by fluctuations that appears at small fluctuation strength and vanishes with increase
of their intensity. As one can observe from Fig. 2d, the system shows hysteretic
properties in case of relatively small intensity of white fluctuations (ε = 20) which
collapses with further increase in fluctuation strength. In studied case, the threshold