Different perturbation theory treatments of the Ginzburg–Landau phase transition model are discussed. This includes a criticism of the perturbative renormalization group (RG) approach and a proposal of a novel method providing critical exponents consistent with the known exact solutions in two dimensions. The new values of critical exponents are discussed and compared to the results of numerica...

We consider a lattice of coupled circle maps, a popular model for the study of mode-locked phenomena. We find that the onset of spatiotemporal intermittency (STI) in this system is analogous to directed percolation (DP), with the transition being to a unique absorbing state for low nonlinearities, and to weakly chaotic absorbing states for high nonlinearities. We find that the complete set of s...

Hysteresis is observed at second order phase transitions. Universal scaling for-mulae for the areas of hysteresis loops are written down. Critical exponents are defined, and related to other exponents for static and dynamic critical phenomena. These relations are verified with Langevin dynamics in both the critical and tricriti-cal mean-field models. A finite-size scaling relation is tested in ...

According to Wilson's theory of critical phenomena, critical exponents are universal functions of d, the dimension of space, and n, the dimension of the symmetry group. SO(5) theory of antiferromagnetism and superconductivity predicts a bicritical point where TN and T~ intersect. By measuring critical exponents close to the bicritical point, and knowing that d = 3, one can experimentally measur...

A general method is given whereby m-connectedness correlation functions can be studied in the percolation problem. The method for m=1 involves calculating the kth power of the correlation function ⟨σ(x)σ(x′)⟩ for a randomly dilute Ising model at nonzero temperature and subsequently averaging over configurations. The final step is to take the limit k→0. This method is tested by reproducing the s...

2014 The negative resistance phenomenon in the unijunction transistor is interpreted as a phase transition, for which the critical exponents 03B2, 03B3’ and 03B4 are measured. Far from the critical point, these exponents have classical values : 03B2 = 1/2, 03B3’ = 1, 03B4 = 3. Close to the critical point, 03B2 and 03B3’ decrease to 0.2 and 0.2 respectively. J. I’hy,viquo LETTRES 41 (t980) L-87 ...

It is shown that the traditionally accepted “Rouse values” for the critical exponents at the gelation transition do not arise from the Rouse model for gelling polymers. The true critical behaviour of the Rouse model for gelling polymers is obtained from spectral properties of the connectivity matrix of the fractal clusters that are formed by the molecules. The required spectral properties are r...

Using a microscopic model and a Green’s function technique we have studied the critical behavior of somemultiferroics such as hexagonal RMnO3. The temperature dependence and the external field dependence of the magnetization and susceptibility are determined. The critical exponents b and g are calculated. Applying the scaling laws a, d, and n are also obtained. The critical exponents are in ver...