William de Castilho and S. R. Salinas
Instituto de Física, Universidade de São Paulo

We analyze the thermodynamic behavior of a ferromagnetic mean-spherical model with three distinct spin components and the addition of Dzyaloshinkii-Moriya interactions. Exact calculations are performed for classical and quantum versions of this lattice model system. We show the onset of space modulated structures at low temperatures. 

William Carreras
Instituto de Física, Universidade de São Paulo

TBA

Guilherme Eduardo Freire Oliveira¹, Christian Maes², and Kasper Meerts²
¹Universidade Federal de Minas Gerais
²Katholieke Universiteit Leuven

We introduce a stochastic multi-photon dynamics on reciprocal space. Assuming isotropy, we derive the diffusion limit for a tagged photon to be a nonlinear Markov process on frequency. The nonlinearity stems from the stimulated emission. In the case of Compton scattering with thermal electrons, the limiting process describes the dynamical fluctuations around the Kompaneets equation. More generally, we construct a photon frequency diffusion process which enables to include nonequilibrium effects. Modifications of the Planck Law may thus be explored, where we focus on the low-frequency regime.

Gabriel Dias Carvalho^1,2 and Pedro Silva Correia^2
1Departamento de Física, Universidade Federal de Pernambuco
²Centro Brasileiro de Pesquisas Físicas

A model of a quantum measurement process is presented: a system consisting of a qubit in a superposition interacts with a measuring apparatus consisting of a N qubit state. Looking at the emerging, effective description of the apparatus given by the action of a coarse-graining channel, we have been able to recover information about the superposition coefficients of the system. We have also been able to visualize the death of quantum correlations between system and apparatus and the death of quantum coherences in the apparatus’ effective state, in the limit of a strong coarse-graining action—a situation akin to decoherence, although it is not necessary to evoke any interaction with the surrounding environment.

Pedro Henrique Mendes and Heitor C. M. Fernandes
Intituto de Física, Universidade Federal do Rio Grande do Sul

In this work we applied two unsupervised machine learning technics in the study of two models, Ising and Potts. Starting from final snapshots of the systems we could reduce the systems dimension and get insights in the
behaviour of the order parameters.

Gustavo O. Heymans¹, N. F. Svaiter¹, and G. Krein^2
1Centro Brasileiro de Pesquisas Físicas
²Instituto de Física Teórica, Universidade do Estado de São Paulo

We investigate the low-temperature behavior of a system in a spontaneously broken symmetry phase described by a Euclidean quantum λΦ⁴_d+1 model with quenched disorder. We study the effects of the disorder linearly coupled to the scalar field using a series representation for the averaged generating functional of connected correlation functions in terms of the moments of the partition function. To deal with the strongly correlated disorder in imaginary time, we employ the equivalence between the model defined in a d-dimensional space with imaginary time with the statistical field theory model defined on a space R^d⊗S¹ with anisotropic quenched disorder. Next, using stochastic differential equations and fractional derivatives, we obtain the Fourier transform of the correlation functions of the disordered system at tree level. In one-loop approximation, we prove that there is a denumerable collection of moments of the partition function that can develop critical behavior. Our main result is that, even with the bulk in the ordered phase, there are many critical compactified lengths that take each of the moments of the partition function from an ordered to a disordered phase. This is a sign of generic scale invariance emergence in the system.

Danilo R. de Assis Elias, Enzo Granato, and Maurice de Koning
Intituto de Física Gleb Wataghin, Universidade Estadual de Campinas

We apply a set of machine-learning (ML) techniques for the global exploration of the phase diagrams of two frustrated 2D Ising models with competing interactions. Based on raw Monte Carlo spin configurations generated for random system parameters, we apply principal-component analysis (PCA) and auto-encoders to achieve dimensionality reduction, followed by clustering using the DBSCAN method and a support-vector machine classifier to construct the transition lines between the distinct phases in both models. The results are in very good agreement with available exact solutions, with the auto-encoders leading to quantitatively superior estimates, even for a data set containing only 1400 spin configurations. In addition, the results suggest the existence of a relationship between the structure of the optimized auto-encoder latent space and physical characteristics of both systems. This indicates that the employed approach can be useful in perceiving fundamental properties of physical systems in situations where a priori theoretical insight is unavailable.

Felipe D. Picoli and V. L. Líbero
Instituto de Física de São Carlos, Universidade de São Paulo

Cerium-based compounds exhibit important magnetic properties like a high magnetic anisotropy and diversity of magnetic orderings. These features result from the moderate localization of their f-state and its strong electronic correlation, in addition, to the crucial spin-orbit interaction [1]. In this direction, the Coqblin-Schrieffer formalism has been used to describe some of these magnetic properties since it incorporates the strong correlation and the spin-orbit interaction on the same foot to obtain an effective interaction energy between two neighbouring f-states [2]. This interaction has been successfully considered, with other sources of anisotropy, like christal-field
effects, to predict the magnetic behaviours of cerium monopnictides and monochalcogenides[1]. However, recent developments have observed and corrected some limitations and inconsistencies of this formalism, like the limitation for ions very far apart and the unphysical absence of the ionic
interchange symmetry [2]. With this new and corrected interaction energy, we have calculated the magnetic properties of some cerium compounds, mainly cerium monopnictides. We could predict the behaviour of the localized magnetic moments and their well-known phase transitions observed
experimentally, reducing the number of parameters required besides the ones already taken into account by the Coqblin-Schrieffer procedure.

[1] Bernard R. Cooper, Robert Siemann, David Yang, Pradeep Thayamballi and Aitava Banerjea, Handbook on the Physics and Chemistry of the Actinides, edited by A. J. Freeman and G. H. Lander, 1985.
[2] F. D. Picoli and V. L. Líbero, JMMM 550, 169062 (2022).

Lair F. Trugilho and L. G. Rizzi
Departamento de Física, Universidade Federal de Viçosa

Temperature-dependent self-assembly processes in finite size volumes, i.e., spontaneous collective organization of a limited number of individual subunits, are present in a vast number of physical and biological systems, including those that involve macromolecular aggregation [1]. Aggregation phenomena have received particular interest due to the relation of protein aggregation with several human diseases, such as Alzheimer and type II diabetes [2]. Although the classical nucleation theory is the most popular approach that one might consider when describing aggregation, there is evidence of failure of that theory for systems where the particles present anisotropic interactions [3,4], as in the case of the amyloid protein aggregates related to the mentioned diseases. In this work, we consider the microcanonical characterization of a simple aggregation model, from which the equilibrium thermostatistics properties associated with the aggregation transition are obtained [5]. Besides, we apply the kinetic theory recently proposed in reference [6] to that model. This theory relates the equilibrium thermostatistics properties, such as latent heats and free-energy barriers, to the temperature-dependent rate constants. In particular, we performed stochastic simulations at different temperatures, from which the rate constants were numerically evaluated, and showed that the temperature-dependent rates estimated by our kinetic approach are in good agreement with the results obtained from the simulations [7]. We believe that our work may provide insights in the general problem of molecular aggregation. In addition, since the kinetic theory discussed here is model independent, it may be applied to more complex systems and provide experimentalists a useful method to access equilibrium thermostatistics properties of the aggregation transition from kinetic data.

[1] M. F. Hagan, G. M. Grason. Equilibrium mechanisms of self-limiting assembly. Rev. Mod. Phys. 93 025008 (2021).
[2] T. P. J. Knowles, M. Vendruscolo, C. M. Dobson. The amyloid state and its association with protein misfolding diseases. Nat. Rev. Mol. Cell Biol. 15 384-396 (2014).
[3] R. Cabriolu, D. Kashchiev, S. Auer. Breakdown of nucleation theory for crystals with strongly anisotropic interactions between molecules. J. Chem. Phys. 137 204903 (2012).
[4] R. J. Bingham, L. G. Rizzi, R. Cabriolu, S. Auer. Non-monotonic supersaturation dependence of the nucleus size of crystals with anisotropically interacting molecules. J. Chem. Phys. 139 241101 (2013).
[5] L. F. Trugilho, L. G. Rizzi. Microcanonical characterization of first order phase transitions in a generalized model for aggregation. J. Stat. Phys. 186 40 (2022).
[6] L. G. Rizzi. Kinetics of first order phase transitions from microcanonical thermostatistics. J. Stat. Mech. 083204 (2020).
[7] L. F. Trugilho, L. G. Rizzi. Shape-free theory for the self-assembly kinetics in macromolecular systems. EPL. 137 57001 (2022).

Emanuel C. Diniz
Universidade do Estado de Mato Grosso

In this work, a sequel of Ref. [1], we investigate the dissipative dynamics of quantum resources such as entanglement, steering, and Bell non-locality in the Heisenberg one dimensional J₁-J₂ spin chain. We employ the microscopic master equation to probe such quantum resources, which give different results depending on the system configuration considering nearest neighbor and next nearest neighbor quantum resources. In particular, steering and Bell non-locality reaching considerable values within the microscopic model to small spin chain and tend to decrease as chain length increases.

[1] E. Diniz, A. Costa, and L. Castelano, Quantum resources of the steady-state of three coupled qubits: Microscopic versus phenomenological model, Physics Letters A 415, 127651 (2021).

Murilo Azambuja
Universidade Federal do Rio Grande do Sul

The Bardeen-Cooper-Schrieffer (BCS) theory is a paradigmatic example in the physics of many-body quantum mechanics. It is based on a model Hamiltonian in which an attractive interaction between electrons with energies near the Fermi energy is postulated, giving rise to a superconducting phase. Even though it succeeded in explaining the low critical temperature metallic superconductors, the theory for itself has some shortcomings. For example, it doesn’t elucidate the microscopic origins of the attractive electron-phonon interaction and also doesn’t include the Coulomb repulsion between electrons, not discussing its role in the formation of a superconducting phase. With the goal of obtaining more information about the microscopic origin of the electron-electron attractive interaction, we apply a Schrieffer-Wolff transformation in a interacting electron and phonon Hamiltonian, arising in an effective electron-electron interaction obtained from the electron-phonon interaction and show that with certain approximations we obtain the model Hamiltonian from the BCS theory. By including a Coulomb repulsion term between electrons in the
interacting electron-phonon Hamiltonian, we obtain the Anderson-Morel model, which shows that the electron-phonon interaction, by having the characteristics of a retarded interaction, plays an essential role in attenuating the effects of the repulsive Coulomb interaction and favors the formation of a superconducting phase.