A modified Ginzburg-Landau model with a screened nonlocal interaction in the quartic term is treated via Wilson's renormalization-group scheme at one-loop order to explore the critical behavior of the paramagnetic-to-ferromagnetic phase transition in perovskite manganites. We find the Fisher exponent η to be O(ε) and the correlation exponent to be ν=1/2+O(ε) through epsilon expansion in the parameter ε=d(c)-d, where d is the space dimension, d(c)=4+2σ is the upper critical dimension, and σ is a parameter coming from the nonlocal interaction in the model Hamiltonian. The ensuing critical exponents in three dimensions for different values of σ compare well with various existing experimental estimates for perovskite manganites with various doping levels. This suggests that the nonlocal model Hamiltonian contains a wide variety of such universality classes.

Employing Wilson's renormalization group scheme, we investigate the critical behaviour of a modified Ginzburg-Landau model with a nonlocal mode-coupling interaction in the quartic term. Carrying out the calculations at one-loop order, we obtain the critical exponents in the leading order of = 4 − d − 2ρ, where ρ is an exponent occurring in the nonlocal interaction term and d is the space dimension. Interestingly, the correlation exponent η is found to be non-zero at one-loop order and the expansion corresponds to an expansion about the tricritical mean-field theory in three dimensions, unlike the conventional Φ 4 theory. The ensuing critical exponents are in good agreement with experimental values for samples close to tricriticality. Our analysis indicates that tricriticality is a feature only in three dimensions.

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We explain the physical motivation for studying the collective coherent motion of large numbers of self-propelled biological organisms. Starting from a well-known discrete model, we discuss the fundamental microscopic mechanisms leading to collective behavior in bird flocks, and how appropriate behavioral rules for the individuals can determine specific features of the aggregation at the group level. We further discuss the theoretical, experimental, and computational effort undertaken to explore this phenomenon together with possible directions for future research in this area.

The construction of honeycombs astonished human being from ancient time due to their perfect geometrical structure. How the hexagonal cells are constructed from fresh circular cells during the cell building process is a matter of long debate. Here we show solely from the thermomechanical properties of self-synthesized beeswax how the honeybees permanently transform the fresh circular cells to rounded hexagons by creating a temperature gradient in the vicinity of the triple junctions of circular cell walls. By assuming conventional Fourier's law of heat conduction and mechanical properties of beeswax, we show via computer simulations that with increasing temperature gradient, the stress on the adjacent circular cell walls increases due to enhanced fusion, leading to the deformation from the original positions of the circular cell walls. The calculated von Mises stresses are found to be significantly larger than the yield stress, indicating the permanent deformation of the circular cell walls to rounded hexagonal shape. This suggests that it is the thermomechanical properties of the building material for which the comb cells take rounded hexagonal shapes.