Related papers: Random Field Induced Order in Low Dimension
Consider the classical XY model in a weak random external field pointing along the Y axis with strength $\epsilon$. We prove that the model defined on $\Z^3$ with nearest neighbor coupling exhibits residual magnetic order in the horizontal…
In this article we prove that a classical $XY$ model subjected to weak i.i.d. random field pointing in a fixed direction exhibits residual magnetic order in $\mathbb{Z}^2$ and aligns perpendicular to the random field direction. The paper is…
Consider the classical XY model in a weak random external field pointing along the $Y$ axis with strength $\epsilon$. We study the behavior of this model as the range of the interaction is varied. We prove that in any dimension $d \geq 2$…
Three-dimensional magnetic ordering transitions are studied theoretically in strongly anisotropic quantum magnets. An external magnetic field can drive quasi-one-dimensional subsystems with a spin gap into a gapless regime, thus inducing…
The critical behavior of the random field $O(N)$ model driven at a uniform velocity is investigated at zero-temperature. From naive phenomenological arguments, we introduce a dimensional reduction property, which relates the large-scale…
The low lying spectrum of the O(n) effective field theory is calculated in the delta-regime in 3 and 4 space-time dimensions using lattice regularization to NNL order. It allows, in particular, to determine, using numerical simulations in…
We consider $n$-component fixed-length order parameter interacting with a weak random field in $d=1,2,3$ dimensions. Relaxation from the initially ordered state and spin-spin correlation functions have been studied on lattices containing…
We investigate three-dimensional O(N) spin models driven with a uniform velocity over a random field. Within a spin-wave approximation, it is shown that in the strong driving regime the model with N=2 exhibits a quasi-long-range order in…
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…
We study the surface scaling behavior of a semi-infinite $d$-dimensional O(N) spin system in the presence of quenched random field and random anisotropy disorders. It is known that above the lower critical dimension $d_{\mathrm{lc}}=4$ the…
Inspired by the works in [1] and [8] we introduce what we call $k$-th-order fluctuation fields and study their scaling limits. This construction is done in the context of particle systems with the property of orthogonal self-duality. This…
We consider a dc-driven damped sine-Gordon model with a small nonlinear spatial-disorder term, onto which a sinusoidal modulation is superimposed. It describes, e.g., a weakly disordered system with a regular grain structure. We demonstrate…
We propose a new higher-dimensional mechanism for solving the Hierarchy Problem. The Weak scale is generated from a large scale of order the Planck scale through an exponential hierarchy. However, this exponential arises not from gauge…
Ground state and low-energy excitations of the quasi-one-dimensional antiferromagnet CuSe$_2$O$_5$ were experimentally studied using bulk magnetization, neutron diffraction, muon spin relaxation and antiferromagnetic resonance measurements.…
Randomly diluted quantum boson and spin models in two dimensions combine the physics of classical percolation with the well-known dimensionality dependence of ordering in quantum lattice models. This combination is rather subtle for models…
We demonstrate that in the system with anisotropic distribution of the defect-induced random local field directions in the n-dimensional space of vector order parameter with the O(n) symmetry, the defect-induced effective anisotropy arises…
We consider classical spin models of two- and three-dimensional spins with continuous symmetry and investigate the effect of a symmetry-breaking unidirectional quenched disorder on the magnetization of the system. We work in the mean-field…
Let R be an o-minimal field with a proper convex subring V. We axiomatize the class of all structures (R,V) such that k_ind, the corresponding residue field with structure induced from R via the residue map, is o-minimal. More precisely, in…
We present an effective field theory method to analyze, in a very general way, models defined over small-world networks. Even if the exactness of the method is limited to the paramagnetic regions and to some special limits, it provides,…
Given an arbitrary (commutative) field K, let V be a linear subspace of M_n(K) consisting of matrices of rank lesser than or equal to some r<n. A theorem of Atkinson and Lloyd states that, if dim V>nr-r+1 and #K>r, then either all the…