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We propose a scaling hypothesis for pattern-forming systems in which modulation of the order parameter results from the competition between a short-ranged interaction and a long-ranged interaction decaying with some power $alpha$ of the inverse distance. With L being a spatial length characterizing the modulated phase, all thermodynamic quantities are predicted to scale like some power of L. The scaling dimensions with respect to L only depend on the dimensionality of the system d and the exponent alpha. Scaling predictions are in agreement with experiments on ultra-thin ferromagnetic films and computational results. Finally, our scaling hypothesis implies that, for some range of values alpha>d, Inverse-Symmetry-Breaking transitions may appear systematically in the considered class of frustrated systems.
We determine the scaling exponents of polymer translocation (PT) through a nanopore by extensive computer simulations of various microscopic models for chain lengths extending up to N=800 in some cases. We focus on the scaling of the average PT time
A scaling theory is developed for diffusion-limited cluster aggregation in a porous medium, where the primary particles and clusters stick irreversibly to the walls of the pore space as well as to each other. Three scaling regimes are predicted, conn
One of the key tasks in physics is to perform measurements in order to determine the state of a system. Often, measurements are aimed at determining the values of physical parameters, but one can also ask simpler questions, such as is the system in s
This paper discusses the elastic behavior of polyelectrolyte networks. The deformation behavior of single polyelectrolyte chains is discussed. It is shown that a strong coupling between interactions and chain elasticity exists. The theory of the comp
We revisit the question of describing critical spin systems and field theories using matrix product states, and formulate a scaling hypothesis in terms of operators, eigenvalues of the transfer matrix, and lattice spacing in the case of field theorie