We study the properties of a model system that exhibits a transition between ferromagnetic and helical order at a Lifshitz point, as interaction parameters R and S compete. Here R JJJ,, and S = J:/J,,, where J , and Jz denote interactions between nearestneighbour and next-nearest-neighbour spin pairs respectively in the z direction, and J, , is a nearest-neighbour interaction between spin pairs...

The extension of strongly anisotropic or dynamical scaling to local scale invariance is investigated. For the special case of an anisotropy or dynamical exponent θ = z = 2, the group of local scale transformation considered is the Schrödinger group, which can be obtained as the non-relativistic limit of the conformal group. The requirement of Schrödinger invariance determines the two-point func...

We study the dynamics of ferromagnetic spin systems quenched from infinite temperature to their critical point. We show that these systems are aging in the long-time regime, i.e., their two-time autocorrelation and response functions and associated fluctuation-dissipation ratio are non-trivial scaling functions of both time variables. This is exemplified by the exact analysis of the spherical m...

We want to study the perturbation growth of an initial seed of an ellipsoidal shape in Top-Hat collapse model of the structure formation in the Modied Chaplygin gas cosmology. Considering reasonable values of the constants and the parameters of the model under study, we can show that a very small deviation from spherical symmetry (ellipsoidal geometry) in the initial seed leads to a nal highly ...