Unconventional critical behaviour in weak ferromagnets Fe2-xMnxCrAl (0 ≤ x < 1)

Recent investigation on weak ferromagnets Fe2-xMnxCrAl (0 ≤ x < 1) reveal the existence of a cluster glass phase (CGP) and a Griffiths-like phase (GP) below and above the ferromagnetic transition temperature (TC), respectively [(2019) Sci. Rep.9 15888]. In this work, the influence of these inhomogeneous phases on the critical behaviour (around TC) of the above-mentioned series of alloys has been investigated in detail. For the parent alloy Fe2CrAl, the critical exponent γ is estimated as ~ 1.34, which lies near to the ordered 3D Heisenberg class, whereas the obtained value of the critical exponent β ~ 0.273 does not belong to any universality class. With increment in Mn concentration, both exponents γ and β increase, where γ and β approach the disordered and ordered 3D Heisenberg class, respectively. The observed deviation of γ and unconventional value of δ can be ascribed to the increment of GP with Mn-concentration. The trend noted for β can be attributed to the increment in CGP regime with an increase in Mn-content. The estimated critical exponents are consistent and reliable as corroborated using the scaling law and equations of state. Our studies indicate that the critical phenomenon of Fe2-xMnxCrAl (0 ≤ x < 1) alloys possibly belong to a separate class, which is not described within the framework of any existing universal model.

Critical behaviour of the stochastic Wilson-Cowan model

Spontaneous brain activity is characterized by bursts and avalanche-like dynamics, with scale-free features typical of critical behaviour. The stochastic version of the celebrated Wilson-Cowan model has been widely studied as a system of spiking neurons reproducing non-trivial features of the neural activity, from avalanche dynamics to oscillatory behaviours. However, to what extent such phenomena are related to the presence of a genuine critical point remains elusive. Here we address this central issue, providing analytical results in the linear approximation and extensive numerical analysis. In particular, we present results supporting the existence of a bona fide critical point, where a second-order-like phase transition occurs, characterized by scale-free avalanche dynamics, scaling with the system size and a diverging relaxation time-scale. Moreover, our study shows that the observed critical behaviour falls within the universality class of the mean-field branching process, where the exponents of the avalanche size and duration distributions are, respectively, 3/2 and 2. We also provide an accurate analysis of the system behaviour as a function of the total number of neurons, focusing on the time correlation functions of the firing rate in a wide range of the parameter space.

Critical behaviour of the stochastic Wilson-Cowan model

Spontaneous brain activity is characterized by bursts and avalanche-like dynamics, with scale-free features typical of critical behaviour. The stochastic version of the celebrated Wilson-Cowan model has been widely studied as a system of spiking neurons reproducing non-trivial features of the neural activity, from avalanche dynamics to oscillatory behaviours. However, to what extent such phenomena are related to the presence of a genuine critical point remains elusive. Here we address this central issue, providing analytical results in the linear approximation and extensive numerical analysis. In particular, we present results supporting the existence of a bona fide critical point, where a second-order-like phase transition occurs, characterized by scale-free avalanche dynamics, scaling with the system size and a diverging relaxation time-scale. Moreover, our study shows that the observed critical behaviour falls within the universality class of the mean-field branching process, where the exponents of the avalanche size and duration distributions are, respectively, -3/2 and -2. We also provide an accurate analysis of the system behaviour as a function of the total number of neurons, focusing on the time correlation functions of the firing rate in a wide range of the parameter space.