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Register a new userQuenched bond randomness in marginal and non-marginal Ising spin models in 2D
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We investigate and contrast, via entropic sampling based on the Wang-Landau algorithm, the effects of quenched bond randomness on the critical behavior of two Ising spin models in 2D. The random bond version of the superantiferromagnetic (SAF) square model with nearest- and next-nearest-neighbor competing interactions and the corresponding version of the simple Ising model are studied and their general universality aspects are inspected by a detailed finite-size scaling (FSS) analysis. We find that, the random bond SAF model obeys weak universality, hyperscaling, and exhibits a strong saturating behavior of the specific heat due to the competing nature of interactions. On the other hand, for the random Ising model we encounter some difficulties for a definite discrimination between the two well-known scenarios of the logarithmic corrections versus the weak universality. Yet, a careful FSS analysis of our data favors the field-theoretically predicted logarithmic corrections.
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We investigate and contrast, via the Wang-Landau (WL) algorithm, the effects of quenched bond randomness on the self-averaging properties of two Ising spin models in 2d. The random bond version of the superantiferromagnetic (SAF) square model with nearest- and next-nearest-neighbor competing interactions and the corresponding version of the simple ferromagnetic Ising model are studied. We find that, the random bond SAF model shows a strong violation of self-averaging, much stronger than that observed in the case of the random bond Ising model. Our analysis of the asymptotic scaling behavior of the variance of the distribution of the sample-dependent pseudocritical temperatures is found to be consistent with the renormalization group prediction of Aharony and Harris. Using this alternative approach, we find estimates of the correlation length exponent $ u$ in agreement with results obtained from the usual finite-size scaling (FSS) methodology.
The rounding of first order phase transitions by quenched randomness is stated in a form which is applicable to both classical and quantum systems: The free energy, as well as the ground state energy, of a spin system on a $d$-dimensional lattice is continuously differentiable with respect to any parameter in the Hamiltonian to which some randomness has been added when $d leq 2$. This implies absence of jumps in the associated order parameter, e.g., the magnetization in case of a random magnetic field. A similar result applies in cases of continuous symmetry breaking for $d leq 4$. Some questions concerning the behavior of related order parameters in such random systems are discussed.
We revisit the concept of marginal stability in glasses, and determine its range of applicability in the context of avalanche-type response to slow external driving. We argue that there is an intimate connection between a pseudo-gap in the distribution of local fields and crackling in systems with long-range interactions. We show how the principle of marginal stability offers a unifying perspective on the phenomenology of systems as diverse as spin and electron glasses, hard spheres, pinned elastic interfaces and the plasticity of soft amorphous solids.
We study the $pm J$ three-dimensional Ising model with a spatially uniaxially anisotropic bond randomness on the simple cubic lattice. The $pm J$ random exchange is applied in the $xy$ planes, whereas in the z direction only a ferromagnetic exchange is used. After sketching the phase diagram and comparing it with the corresponding isotropic case, the system is studied, at the ferromagnetic-paramagnetic transition line, using parallel tempering and a convenient concentration of antiferromagnetic bonds ($p_z=0 ; p_{xy}=0.176$). The numerical data point out clearly to a second-order ferromagnetic-paramagnetic phase transition belonging in the same universality class with the 3d random Ising model. The smooth finite-size behavior of the effective exponents describing the peaks of the logarithmic derivatives of the order parameter provides an accurate estimate of the critical exponent $1/ u=1.463(3)$ and a collapse analysis of magnetization data gives an estimate $beta/ u=0.516(7)$. These results, are in agreement with previous studies and in particular with those of the isotropic $pm J$ three-dimensional Ising at the ferromagnetic-paramagnetic transition line, indicating the irrelevance of the introduced anisotropy.
Shearing stresses can change the volume of a material via a nonlinear effect known as shear dilatancy. We calculate the elastic dilatancy coefficient of soft sphere packings and random spring networks, two canonical models of marginal solids close to their rigidity transition. We predict a dramatic enhancement of dilatancy near rigidity loss in both materials, with a surprising distinction: while packings expand under shear, networks contract. We show that contraction in networks is due to the destabilizing influence of increasing hydrostatic or uniaxial loads, which is counteracted in packings by the formation of new contacts.
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