skip to main content


Title: Deep learning on the 2-dimensional Ising model to extract the crossover region with a variational autoencoder
The 2-dimensional Ising model on a square lattice is investigated with a variational autoencoder in the non-vanishing field case for the purpose of extracting the crossover region between the ferromagnetic and paramagnetic phases. The encoded latent variable space is found to provide suitable metrics for tracking the order and disorder in the Ising configurations that extends to the extraction of a crossover region in a way that is consistent with expectations. The extracted results achieve an exceptional prediction for the critical point as well as agreement with previously published results on the configurational magnetizations of the model. The performance of this method provides encouragement for the use of machine learning to extract meaningful structural information from complex physical systems where little a priori data is available.  more » « less
Award ID(s):
1728457
NSF-PAR ID:
10188584
Author(s) / Creator(s):
; ;
Date Published:
Journal Name:
Scientific reports
Volume:
10
ISSN:
0068-1261
Page Range / eLocation ID:
13047
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. null (Ed.)
    For the spin crossover coordination polymer [Fe(L1)(bipy)] n (where L1 is a N 2 O 2 2− coordinating Schiff base-like ligand bearing a phenazine fluorophore and bipy = 4,4′-bipyridine), there is compelling additional evidence of a spin state transition. Both Fe 2p X-ray absorption and X-ray core level photoemission spectroscopies confirm that a spin crossover takes place, as observed by magnetometry. Yet the details of the temperature dependent changes of the spin state inferred from both X-ray absorption and X-ray core level photoemission, differ from magnetometry, particularly with regard to the apparent critical transition temperatures and the cooperative nature of the curve progression in general. Comparing the experimental spin crossover data to Ising model simulations, a transition activation energy in the region of 160 to 175 meV is indicated, along with a nonzero exchange J . Overall, the implication is that there may be perturbations to the bistability of spin states, that are measurement dependent or that the surface differs from the bulk with regard to the cooperative effects observed upon spin transition. 
    more » « less
  2. The exponential suppression of macroscopic quantum tunneling (MQT) in the number of elements to be reconfigured is an essential element of broken symmetry phases. This suppression is also a core bottleneck in quantum algorithms, such as traversing an energy landscape in optimization, and adiabatic state preparation more generally. In this work, we demonstrate exponential acceleration of MQT through Floquet engineering with the application of a uniform, high frequency transverse drive field. Using the ferromagnetic phase of the transverse field Ising model in one and two dimensions as a prototypical example, we identify three phenomenological regimes as a function of drive strength. For weak drives, the system exhibits exponentially decaying tunneling rates but robust magnetic order; in the crossover regime at intermediate drive strength, we find polynomial decay of tunnelling alongside vanishing magnetic order; and at very strong drive strengths both the Rabi frequency and time-averaged magnetic order are approximately constant with increasing system size. We support these claims with extensive full wavefunction and tensor network numerical simulations, and theoretical analysis. An experimental test of these results presents a technologically important and novel scientific question accessible on NISQ-era quantum computers. 
    more » « less
  3. Abstract Compact domain features have been observed in spin crossover [Fe{H 2 B(pz) 2 } 2 (bipy)] molecular thin film systems via soft x-ray absorption spectroscopy and photoemission electron microscopy. The domains are in a mixed spin state that on average corresponds to roughly 2/3 the high spin occupation of the pure high spin state. Monte Carlo simulations support the presence of intermolecular interactions that can be described in terms of an Ising model in which interactions beyond nearest-neighbors cannot be neglected. This suggests the presence of short-range order to permit interactions between molecules beyond nearest neighbor that contribute to the formation of largely high spin state domains structure. The formation of a spin state domain structure appears to be the result of extensive cooperative effects. 
    more » « less
  4. We investigate quasi-two-dimensional buckled colloidal monolayers on a triangular lattice with tunable depletion interactions. Without depletion attraction, the experimental system provides a colloidal analog of the well-known geometrically frustrated Ising antiferromagnet [Y. Han et al., Nature 456, 898–903 (2008)]. In this contribution, we show that the added depletion attraction can influence both the magnitude and sign of an Ising spin coupling constant. As a result, the nearest-neighbor Ising “spin” interactions can be made to vary from antiferromagnetic to para- and ferromagnetic. Using a simple theory, we compute an effective Ising nearest-neighbor coupling constant, and we show how competition between entropic effects permits for the modification of the coupling constant. We then experimentally demonstrate depletion-induced modification of the coupling constant, including its sign, and other behaviors. Depletion interactions are induced by rod-like surfactant micelles that change length with temperature and thus offer means for tuning the depletion attraction in situ. Buckled colloidal suspensions exhibit a crossover from an Ising antiferromagnetic to paramagnetic phase as a function of increasing depletion attraction. Additional dynamical experiments reveal structural arrest in various regimes of the coupling-constant, driven by different mechanisms. In total, this work introduces novel colloidal matter with “magnetic” features and complex dynamics rarely observed in traditional spin systems. 
    more » « less
  5. Wootters, Mary ; Sanita, Laura (Ed.)
    The Swendsen-Wang algorithm is a sophisticated, widely-used Markov chain for sampling from the Gibbs distribution for the ferromagnetic Ising and Potts models. This chain has proved difficult to analyze, due in part to the global nature of its updates. We present optimal bounds on the convergence rate of the Swendsen-Wang algorithm for the complete d-ary tree. Our bounds extend to the non-uniqueness region and apply to all boundary conditions. We show that the spatial mixing conditions known as Variance Mixing and Entropy Mixing, introduced in the study of local Markov chains by Martinelli et al. (2003), imply Ω(1) spectral gap and O(log n) mixing time, respectively, for the Swendsen-Wang dynamics on the d-ary tree. We also show that these bounds are asymptotically optimal. As a consequence, we establish Θ(log n) mixing for the Swendsen-Wang dynamics for all boundary conditions throughout the tree uniqueness region; in fact, our bounds hold beyond the uniqueness threshold for the Ising model, and for the q-state Potts model when q is small with respect to d. Our proofs feature a novel spectral view of the Variance Mixing condition inspired by several recent rapid mixing results on high-dimensional expanders and utilize recent work on block factorization of entropy under spatial mixing conditions. 
    more » « less