The relation between differential geometry of surfaces and some Heisenberg ferromagnet models is considered.
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43 results for “ferromagnets”
Geometrical flows (GF) play an important role in modern mathematics and physics. In this letter we have considered some integrable isotropic GF -- Ricci flows (RF) and mean curvature flows (MCF) -- which are related with integrable Heisenberg ferromagnets. In 2+1 dimensions, these GF have a singularity at .
Exact asymmetric Skyrmion in anisotropic ferromagnet and its helimagnetic applicationcond-mat.stat-mech
Topological Skyrmions as intricate spin textures were observed experimentally in helimagnets on 2d plane. Theoretical foundation of such solitonic states to appear in pure ferromagnetic model, as exact solutions expressed through any analytic function, was made long ago by Belavin and Polyakov (BP). We propose an innov…
The paper studies structure detection in high-temperature ferromagnetic models.
problem Distinguishing between empty models and models with a specific subgraph structure.
method Matching upper and lower bounds for minimax testing, and computational hardness results.
result Arboricity drives the testability of the problem, and there are no polynomial time tests under certain conditions.
Study motion of discrete interfaces on triangular lattice using Almgren, Taylor, and Wang's approach.
problem Motion of discrete interfaces on triangular lattice driven by ferromagnetic interactions.
method Coupling Almgren, Taylor, and Wang's minimizing movements approach with Braides, Gelli, and Novaga's discrete-to-continuum analysis.
result Limit motion of origin-symmetric convex hexagons compared to crystalline curvature evolution.
This paper explores the information-theoretic limitations of graph property testing in zero-field Ising models. Instead of learning the entire graph structure, sometimes testing a basic graph property such as connectivity, cycle presence or maximum clique size is a more relevant and attainable objective. Since property…
Graphical models are a rich language for describing high-dimensional distributions in terms of their dependence structure. While there are algorithms with provable guarantees for learning undirected graphical models in a variety of settings, there has been much less progress in the important scenario when there are lat…
Belief propagation quickly converges to global optima for ferromagnetic Ising models.
problem Understanding convergence of belief propagation on graphs with cycles.
method Natural initialization and analysis of Ising models on arbitrary graphs.
result Belief propagation converges quickly to the global optimum of the Bethe free energy for ferromagnetic Ising models.
We study the motion of discrete interfaces driven by ferromagnetic interactions in a two-dimensional periodic environment by coupling the minimizing movements approach by Almgren, Taylor and Wang and a discrete-to-continuous analysis. The case of a homogeneous environment has been recently treated by Braides, Gelli and…
Algorithm learns RBMs with arbitrary external fields, improving on previous constraints.
problem Learning RBMs with arbitrary external fields, improving on previous constraints.
method Greedy algorithm that maximizes covariance between observed nodes sharing latent neighbors.
result Algorithm can learn RBMs with arbitrary external fields, improving on previous constraints.
We study long wave limits for general Schrodinger maps systems into Kahler manifolds with a constraining potential vanishing on a Lagrangian submanifold. We obtain KdV type systems set on the tangent space of the submanifold. Our general theory is applied to study the long wave limit of the Gross-Pitaevskii equation, a…
Approximate algorithms for structured prediction problems---such as LP relaxations and the popular alpha-expansion algorithm (Boykov et al. 2001)---typically far exceed their theoretical performance guarantees on real-world instances. These algorithms often find solutions that are very close to optimal. The goal of thi…
Dynamic sampling from changing graphical models.
problem Sampling from a changing graphical model.
method Parallel Las Vegas algorithm for dynamic sampling.
result First dynamic sampling algorithms for Ising and hardcore models.
This paper introduces a new specialized algorithm for equilibrium Monte Carlo sampling of binary-valued systems, which allows for large moves in the state space. This is achieved by constructing self-avoiding walks (SAWs) in the state space. As a consequence, many bits are flipped in a single MCMC step. We name the alg…
Generalized belief propagation converges to optimal solutions on graphs with motifs.
problem Understanding belief propagation on loopy graphs.
method Study of generalized belief propagation on graphs with motifs.
result Generalized belief propagation converges to the global optimum of the Bethe free energy.
The Gibbs sampler is a particularly popular Markov chain used for learning and inference problems in Graphical Models (GMs). These tasks are computationally intractable in general, and the Gibbs sampler often suffers from slow mixing. In this paper, we study the Swendsen-Wang dynamics which is a more sophisticated Mark…
Quantum annealing is a generic solver of the optimization problem that uses fictitious quantum fluctuation. Its simulation in classical computing is often performed using the quantum Monte Carlo simulation via the Suzuki--Trotter decomposition. However, the negative sign problem sometimes emerges in the simulation of q…
We analyze income tax evasion dynamics in a standard model of statistical mechanics, the Ising model of ferromagnetism. However, in contrast to previous research, we use an inhomogeneous multi-dimensional Ising model where the local degrees of freedom (agents) are subject to a specific social temperature and coupled to…
Study null curves and their motion in 3D flat space-time, leading to integrable hierarchies.
problem Understanding null curves and their motion in 3D flat space-time.
method Analyzing the motion of null curves and their surfaces, deriving integrability conditions and hierarchies.
result Obtained one- and two-soliton surfaces associated with the MKdV equation, showing singularities in finite time.
We present a method for scalable and fully 3D magnetic field simultaneous localisation and mapping (SLAM) using local anomalies in the magnetic field as a source of position information. These anomalies are due to the presence of ferromagnetic material in the structure of buildings and in objects such as furniture. We …
We study the motion of discrete interfaces driven by ferromagnetic interactions in a two-dimensional low-contrast periodic environment, by coupling the minimizing movements approach by Almgren, Taylor and Wang and a discrete-to-continuum analysis. As in a recent paper by Braides and Scilla dealing with high-contrast pe…
Model analyzes corruption dynamics on an Ising lattice.
problem Tackles corruption dynamics on an Ising lattice.
method Formulated as an Ising lattice model with stochastic Markov process.
result Demonstrates different asymptotic states of corruption networks.
Paper presents a privacy-preserving algorithm for estimating peer effects using the Ising model.
problem Privacy concerns in estimating peer effects using network data.
method Developed a -differentially private algorithm using Ising model.
result Established regret bounds and validated performance on synthetic and real-world networks.
Prior distributions of binarized natural images are learned by using a Boltzmann machine. According the results of this study, there emerges a structure with two sublattices in the interactions, and the nearest-neighbor and next-nearest-neighbor interactions correspondingly take two discriminative values, which reflect…
Optimal SQ bounds for learning binary product distributions and Ising models.
problem Learning binary product distributions and Ising models robustly.
method Statistical Query (SQ) lower bounds for robust learning.
result Optimal SQ lower bounds match known algorithm error guarantees.
Unveiling phase transitions with machine learningcond-mat.str-el
Machine learning identifies phase transitions in condensed matter physics.
problem Classifying phase transitions in condensed matter physics.
method Unsupervised and supervised machine learning techniques applied to the Ising model.
result Machine learning can detect multiple phases and regions within the paramagnetic phase.
We prove a mapping between dual and primal factor graph marginals for efficient estimation.
problem Efficient estimation of marginal densities in factor graphs.
method Local mappings derived from Fourier transforms of local factors, applied to Ising and Potts models.
result Marginal densities can be more accurately estimated in the dual domain.
Paper optimizes change detection in unnormalized distributions.
problem Detecting changes in unnormalized pre- and post-change distributions.
method Log-Partition Approximation Cumulative Sum (LPA-CUSUM) algorithm based on thermodynamic integration.
result Asymptotically optimal performance achieved through unbiased estimation of CUSUM statistics.
Emergence of a finite-size-scaling function in the supervised learning of the Ising phase transitioncond-mat.stat-mech
A neural network model predicts the critical point of the Ising phase transition.
problem Predicting the critical point of the Ising phase transition using supervised learning.
method Proposed a minimal one-free-parameter neural network model to describe the supervised learning problem for the Ising model.
result Just one free parameter is enough to describe the universal finite-size-scaling function in the network output.
Inspired by the bankruptcy of Lehman Brothers and its consequences on the global financial system, we develop a simple model in which the Lehman default event is quantified as having an almost immediate effect in worsening the credit worthiness of all financial institutions in the economic network. In our stylized desc…
Mapping the magnetic field using a magnetometer array with noisy input Gaussian process regressionstat.ML
Improves magnetic field mapping using an array of magnetometers with noisy input.
problem Improving magnetic field maps in indoor environments with noisy magnetometer data.
method Uses Gaussian process regression with an array of magnetometers, incorporating known array positions and relative magnetometer locations.
result The method produces higher quality magnetic field maps compared to using a single magnetometer.
In this paper we investigate the computational complexity of learning the graph structure underlying a discrete undirected graphical model from i.i.d. samples. We first observe that the notoriously difficult problem of learning parities with noise can be captured as a special case of learning graphical models. This lea…
This article considers a model for alternative processes for securities prices and compares this model with actual return data of several securities. The distributions of returns that appear in the model can be Gaussian as well as non-Gaussian; in particular they may have two peaks. We consider a discrete Markov chain …
Symmetry-electronic fingerprints reveal competing magnetic phases in two-dimensional materialscond-mat.mtrl-sci
Symmetry-electronic fingerprints reveal competing magnetic phases in two-dimensional materials.
problem Predicting magnetic ground states, moments, and anisotropy in two-dimensional magnets.
method Introduce the symmetry-electronic fingerprint (SEF), a physically interpretable representation that encodes crystallographic symmetry operations, Wyckoff-site geometry, and site-resolved electronic structure.
result SEF-trained models accurately classify magnetic ordering and regress moments alongside anisotropy energies.
Local mappings relate dual and primal factor graphs for efficient marginal probability estimation.
problem Efficient estimation of marginal probabilities in statistical physics models.
method Local mappings based on Fourier transform of local factors, applied to Ising, Potts, and clock models.
result Local extrema of fixed points are at phase transition points, and the mapping facilitates efficient estimation.
We propose a formula of time-series prediction by means of three states random field Ising model (RFIM). At the economic crisis due to disasters or international disputes, the stock price suddenly drops. The macroscopic phenomena should be explained from the corresponding microscopic view point because there are existi…
Adversarial inference on tree models is possible with limited corruption, improving on Kesten-Stigum threshold.
problem Posterior inference on tree-structured graphical models in the presence of adversarial corruption.
method Dynamic programming via belief propagation, constrained adversarial corruption.
result Belief propagation can perform accurate inference with limited adversarial corruption.
We consider the problem of approximating partition functions for Ising models. We make use of recent tools in combinatorial optimization: the Sherali-Adams and Lasserre convex programming hierarchies, in combination with variational methods to get algorithms for calculating partition functions in these families. These …
New algorithm for learning RBMs with sparse latent variables.
problem Learning RBMs with sparse latent variables efficiently.
method Algorithm with time complexity O(n^(2^s+1)) for sparse RBMs.
result Improves learning time for RBMs with sparse latent variables.
New algorithm samples from Ising models efficiently, even with outliers.
problem Sampling from Ising models with general interaction matrices.
method Combines MCMC and variational inference techniques.
result First polynomial time sampling algorithms for low-rank Ising models.
GE-autoencoder identifies spontaneous symmetry breaking in systems.
problem Locating phase boundaries and identifying spontaneously broken symmetries in systems.
method Group-equivariant autoencoder using group theory to constrain parameters and learn invariant order parameters.
result GE-autoencoder accurately determines spontaneous symmetry breaking and estimates critical temperatures more efficiently.
Predictions of Electromotive Force of Magnetic Shape Memory Alloy (MSMA) Using Constitutive Model and Generalized Regression Neural Networkcond-mat.mtrl-sci
Model predicts EMF of Ni-Mn-Ga MSMA, improved with GRNN.
problem Predicting the electromotive force (EMF) of Ni-Mn-Ga MSMA under various conditions.
method Developed a new constitutive model for Ni-Mn-Ga single crystals, incorporating magnetic easy axis offset. Used GRNN to enhance model predictions.
result GRNN improves model predictions of EMF, capturing more experimental features.
This paper tackles exact recovery of clusters in a stochastic Ising model on a SBM graph.
problem Recovering clusters in a stochastic Ising model on a SBM graph.
method Proposes a Stochastic Ising Block Model (SIBM) and establishes a sharp threshold for exact recovery.
result Sharp threshold for exact recovery of clusters in SIBM, with time complexity for .