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The motivation of this thesis is to understand the ferromagnetic properties of LaCoO3 strained films. For this purpose, we will make use of Monte Carlo simulations, as well as an Extended Ising model directly derived from microscopic theory. Firstly, the most important features of our Heat Bath algorithm and the data analysis techniques employed for the correct treatment of correlated data will be presented. Then, starting from the simplest models, we will perform numerical simulations using a Julia environment to study the macroscopic quantities of our systems and benchmark them with the theoretical expressions. In order to interpret the outcome of the simulations for our Extended Ising model, we will develop a mathematical model based on the mean field theory that reproduces the physical behaviour of the system. Furthermore, based on our results, we will discuss that an additional 3D interaction term is required to obtain a net polarization in both two and three-dimensional structures, and we will postulate the 4s interaction as the origin of ferromagnetism in LaCoO3 films. La motivación de esta tesis es comprender las propiedades ferromagnéticas del LaCoO3 en películas tensas. Para ello, haremos uso de simulaciones Monte Carlo, así como un modelo de Ising extendido directamente derivado de la teoría microscópica. En primer lugar, se presentarán las características más importantes de nuestro algoritmo Heat Bath y las técnicas empleadas para el correcto tratamiento de los datos correlacionados. Luego, partiendo de los modelos más simples, realizaremos simulaciones numéricas usando un entorno de Julia para estudiar las cantidades macroscópicas de nuestros sistemas y compararlas con las expresiones teóricas. Para interpretar el resultado de las simulaciones en nuestro modelo de Ising extendido, desarrollaremos un modelo matemático basado en la teoría del campo medio que reproduce el comportamiento físico del sistema. Además, en base a nuestros resultados, discutiremos que se requiere una interacción 3D adicional para obtener una polarización neta en las estructuras tanto en dos como en tres dimensiones y postularemos la interacción 4s como el origen del ferromagnetismo en películas de LaCoO3. La motivació d'aquesta tesi és entendre les propietats ferromagnètiques del LaCoO3 en pel·lícules tenses. Per a això, farem ús de les simulacions de Monte Carlo, així com un model de Ising estès derivat directament de la teoria microscòpica. En primer lloc, es presentaran les característiques més importants del nostre algorisme de Heat Bath i les tècniques emprades per al correcte tractament de les dades correlacionades. Després, partint dels models més senzills, realitzarem simulacions numèriques utilitzant un entorn de Julia per estudiar les magnituds macroscòpiques dels nostres sistemes i compara'ls amb les expressions teòriques. Per interpretar el resultat de les simulacions per al nostre model Ising estès, desenvoluparem un model matemàtic basat en la teoria del camp mitjà que reprodueix el comportament físic del sistema. A més, a partir dels nostres resultats, discutirem que es requereix un terme de interacció 3D addicional per obtenir una polarització neta en estructures tant en dos com en tres dimensions, i postularem la interacció 4s com l'origen del ferromagnetisme a les pel·lícules LaCoO3.

Treballs Finals de Grau de Física, Facultat de Física, Universitat de Barcelona, Curs: 2022, Tutor: Bruno Juliá Díaz, We give a short introduction to quantum annealing in the transverse Ising model and formulate the maximum clique problem in this setting. We then brie y show how problems are actually implemented in D-Wave's annealers through the idea of minor-embeddings and chains. We also provide simulations for a small problem and actual results on D-Wave's annealers for larger instances as well as the dependence of the success rate on different parameters.

Correction to: Communications Physics https://doi.org/10.1038/s42005-020-00492-1, published online 4 December 2020.

Cyclic fluid-fluid displacements in disordered media feature hysteresis, multivaluedness, and memory properties in the pressure-saturation relationship. Quantitative understanding of the underlying pore-scale mechanisms and their extrapolation across scales constitutes a major challenge. Here we find that the capillary action of a single constriction in the fluid passage contains the key features of hysteresis. This insight forms the building block for an ab initio model that provides the quantitative link between the microscopic capillary physics, spatially-extended collective events (Haines jumps) and large-scale hysteresis. The mechanisms identified here apply to a broad range of problems in hydrology, geophysics and engineering., R.H. acknowledges partial support from the Israeli Science Foundation (#ISF-867/13); M.D. and J.O. received support from the Spanish Ministry of Science and Innovation through the project HydroPore (PID2019-106887GB-C31 and C32). R.P. and J.O. received support from AGAUR (Generalitat de Catalunya) through grant 2017-SGR-1061.

Treballs Finals de Grau de Física, Facultat de Física, Universitat de Barcelona, Curs: 2020, Tutor: Antoni Planes i Vila, We study the dynamic behavior of the Ising model under an oscillating magnetic field in the mean-field approximation. A dynamic phase transition causing a spontaneous symmetry breaking of the hysteresis loop arises due to the competition between the timescales associated with the spin relaxation and the oscillating field. A dynamic order parameter measuring the asymmetry of the hysteresis loop is defined and its critical behavior is explored. The critical exponents are found to match those of the equilibrium transition once the thermodynamic variables are replaced with certain dynamic variables.

Treballs Finals de Grau de Física, Facultat de Física, Universitat de Barcelona, Curs: 2019, Tutor: José Ignacio Latorre, The phase diagram of the quantum Axial Next-Nearest Neighbour Ising model is studied with and without transverse field, in order to locate the maximally frustrated point. AVariational Quantum Eigensolver has been implemented for 4, 8 and 12 qubits, to compute the ground state energy of this Hamiltonian. Besides, the Solovay-Kitaev theorem is introduced in order to analyze how the error of the energy scales with the number of gates of the circuit

Treballs Finals de Grau de Física, Facultat de Física, Universitat de Barcelona, Curs: 2018, Tutor: Bruno Julià-Díaz, In this work we perform numerical simulations of a quantum annealing procedure to find the ground state of a target Hamiltonian. By using this technique one starts from an Ising Hamiltonian with a transverse field that forces the spins to point in the x direction. The field is removed slowly with time, the purpose of this is to carry an adiabatic transition from the transverse-field Hamiltonian to the target Hamiltonian. In order to prove the functionality of quantum annealing we will introduce two terms to quantify the success of the protocol

We introduce a novel random field Ising model, grounded on experimental observations, to assess the importance of metric correlations in cortical circuits in vitro. Metric correlations arise from both the finite axonal length and the heterogeneity in the spatial arrangement of neurons. The experiments consider the response of neuronal cultures to an external electric stimulation for a gradually weaker connectivity strength between neurons, and in cultures with different spatial configurations. The model can be analytically solved in the metric-free, mean-field scenario. The presence of metric correlations precipitates a strong deviation from the mean field. Null models of the same networks that preserve the distribution of connections recover the mean field. Our results show that metric-inherited correlations in spatial networks dominate the connectivity blueprint, mask the actual distribution of connections, and may emerge as the asset that shapes network dynamics.

To understand the origin of the dynamical transition, between high temperature exponential relaxation and low temperature nonexponential relaxation, that occurs well above the static transition in glassy systems, a frustrated spin model, with and without disorder, is considered. The model has two phase transitions, the lower being a standard spin glass transition (in presence of disorder) or fully frustrated Ising (in absence of disorder), and the higher being a Potts transition. Monte Carlo results clarify that in the model with (or without) disorder the precursor phenomena are related to the Griffiths (or Potts) transition. The Griffiths transition is a vanishing transition which occurs above the Potts transition and is present only when disorder is present, while the Potts transition which signals the effect due to frustration is always present. These results suggest that precursor phenomena in frustrated systems are due either to disorder and/or to frustration, giving a consistent interpretation also for the limiting cases of Ising spin glass and of Ising fully frustrated model, where also the Potts transition is vanishing. This interpretation could play a relevant role in glassy systems beyond the spin systems case., Comment: Completely rewritten. New data. New results

S:L'objectiu principal d'aquesta tesi és aprofundir en l'estudi dels models microscòpics que permeten estudiar la histèresi. Aquest fenomen està present en moltes àrees de la física i ha despertat l'interès de molts investigadors al llarg de la història.Entre tots els sistemes que presenten histèresis, ens centrem en els que tenen un comportament atèrmic. En aquests, la histèresi no és conseqüència d'una competició entre la velocitat de conducció de la força externa i la velocitat de relaxació del sistema i per tant, s'obté una histèresi que no depèn del ritme de variació de la força externa. En aquests sistemes atèrmics, la histèresi és deguda a la presència d'un escenari molt complex d'energia lliure amb un gran número d'estats metastables separats amb unes barreres energètiques molt altes. Aquestes barreres energètiques altes fan que el paper de les fluctuacions tèrmiques sigui negligible i que el sistema només pugui evolucionar quan el conduïm amb un camp extern, presentant una evolució amb una dinàmica d'allaus.En la tesi s'aprofundeix en un dels models microscòpics que ha servit per modelitzar el comportament dels sistemes ferromagnètics reals. Aquest model s'obté fent una extensió del model d'Ising habitual i s'anomena model d'Ising amb camps aleatoris (RFIM). Malgrat que es pot estudiar el comportament d'equilibri, els nostres estudis han estat enfocats a estudiar-lo amb una dinàmica metastable a temperatura zero que serveix per modelitzar el comportament dels sistemes atèrmics. La tesi esta dividida en quatre blocs:i) Un primer bloc en el qual es fa una introducció a la termodinàmica dels sistemes magnètics (capítol 1) i un estudi detallat del RFIM considerant tant el cas d'equilibri com la dinàmica metastable (capítol 2). ii) Un segon bloc on es desenvolupen els càlculs analítics que s'han realitzat del model. S'obtenen les expressions analítiques dels termes energètics del RFIM amb dinàmica metastable "1-spin-flip" sobre xarxes de Bethe (capítol 3). També s'obte l'expressió analítica de la imantació del RFIM amb dinàmica metastable "2-spin-flip" sobre una cadena unidimensional(xarxa de Bethe amb connectivicat dos) i es demostra l'aparició d'una transició de fase fora de l'equilibri quan s'utilitza una xarxa de Bethe amb connectivitat tres (capítol 4). iii)El tercer bloc està dedicat a l'estudi d'algunes propietats del model. Es realitza un estudi detallat del RFIM diluït que s'obté introduint vacants al sistema (capítol 5). Per altra banda també s'estudien les propietats estadístiques dels "pinning fields" que són els causants de l'escenari complex d'energia lliure i per tant de la histèresi en els sistemes atèrmics (capítol 6).iv) L'últim bloc està dedicat a utilitzar el model per interpretar algunes observacions experimentals. En el capítol 7 s'utilitza una petita modificació del RFIM per donar una explicació senzilla del fenomen de l'"Exchange Bias" i en el capítol 8 s'estudien les propietats del RFIM quan la variable de control passa a ser la imantació enlloc del camp extern., THESIS ABSTRACT:The main goal of this thesis is to perform a deep study of some microscopic models that allow hystereis to be studied. This phenomenon is ubiquitous in many areas of physics and has attracted the attention of researchers for a long time.Among all systems that have hysteresis we will focus on those that have an athermic behaviour. In these cases hysteresis is not due to a competition between the driving force rate and the system relaxation rate, and therefore these systems have a rate independent hysteresis. In athermic systems, hysteresis originates from the existence of very complex free energy scenario with high energy barriers. These high energy barriers cause that thermal fluctuations are completely negligible, and the system can only evolve when it is driven by an external field, showing an avalanche-like dynamics.In this thesis we focus on the random-field Ising model (RFIM) which has been used to model the behaviour of real ferromagnetic systems. RFIM is an extension of the well-known Ising model. His equilibrium behaviour has been widely studied and we focus on the metastable dynamics at zero temperature which is useful to model athermic systems. We present new analytical results and study some properties and experimental applications.

We investigate the influence of the driving mechanism on the hysteretic response of systems with athermal dynamics. In the framework of local-mean field theory at finite temperature (but neglecting thermallly activated processes), we compare the rate-independent hysteresis loops obtained in the random field Ising model (RFIM) when controlling either the external magnetic field $H$ or the extensive magnetization $M$. Two distinct behaviors are observed, depending on disorder strength. At large disorder, the $H$-driven and $M$-driven protocols yield identical hysteresis loops in the thermodynamic limit. At low disorder, when the $H$-driven magnetization curve is discontinuous (due to the presence of a macroscopic avalanche), the $M$-driven loop is re-entrant while the induced field exhibits strong intermittent fluctuations and is only weakly self-averaging. The relevance of these results to the experimental observations in ferromagnetic materials, shape memory alloys, and other disordered systems is discussed., 11 pages, 11 figures

We study the hysteretic evolution of the random field Ising model (RFIM) at T=0 when the magnetization M is controlled externally and the magnetic field H becomes the output variable. The dynamics is a simple modification of the single-spin-flip dynamics used in the H-driven situation and consists in flipping successively the spins with the largest local field. This allows to perform a detailed comparison between the microscopic trajectories followed by the system with the two protocols. Simulations are performed on random graphs with connectivity z=4 (Bethe lattice) and on the 3-D cubic lattice. The same internal energy U(M)is found with the two protocols when there is no macroscopic avalanche and it does not depend on whether the microscopic states are stable or not. On the Bethe lattice, the energy inside the macroscopic avalanche also coincides with the one that is computed analytically with the H-driven algorithm along the unstable branch of the hysteresis loop. The output field, defined here as dU/dM, exhibits very large fluctuations with the magnetization and is not self-averaging. Relation to the experimental situation is discussed., 11 pages, 13 figures

The influence of vacancy concentration on the behavior of the three-dimensional random field Ising model with metastable dynamics is studied. We have focused our analysis on the number of spanning avalanches which allows us a clear determination of the critical line where the hysteresis loops change from continuous to discontinuous. By a detailed finite-size scaling analysis we determine the phase diagram and numerically estimate the critical exponents along the whole critical line. Finally, we discuss the origin of the curvature of the critical line at high vacancy concentration.

We study the non-equilibrium behavior of the three-dimensional Gaussian random-field Ising model at T=0 in the presence of a uniform external field using a 2-spin-flip dynamics. The deterministic, history-dependent evolution of the system is compared with the one obtained with the standard 1-spin-flip dynamics used in previous studies of the model. The change in the dynamics yields a significant suppression of coercivity, but the distribution of avalanches (in number and size) stays remarkably similar, except for the largest ones that are responsible for the jump in the saturation magnetization curve at low disorder in the thermodynamic limit. By performing a finite-size scaling study, we find strong evidence that the change in the dynamics does not modify the universality class of the disorder-induced phase transition., Comment: 9 pages, 10 figures

We consider the analytic solution of the zero temperature hysteresis in the random field Ising model on a Bethe lattice of coordination number $z$, and study how it approaches the mean field solution in the limit z-> \infty. New analytical results concerning the energy of the system along the hysteresis loop and first order reversal curves (FORC diagrams) are also presented., 4 pages, 4 figures, Submitted to PRB

We present a simple model that allows hysteresis loops with exchange bias to be reproduced. The model is a modification of the T=0 random field Ising model driven by an external field and with synchronous local relaxation dynamics. The main novelty of the model is that a certain fraction f of the exchange constants between neighbouring spins is enhanced to a very large value J_E. The model allows the dependence of the exchange bias and other properties of the hysteresis loops to be analyzed as a function of the parameters of the model: the fraction f of enhanced bonds, the amount of the enhancement J_E and the amount of disorder which is controlled by the width sigma of the Gaussian distribution of the random fields., Comment: 8 pages, 11 figures

The behaviour of the Random Anisotropy Ising model at T=0 under local relaxation dynamics is studied. The model includes a dominant ferromagnetic interaction and assumes an infinite anisotropy at each site along local anisotropy axes which are randomly aligned. Two different random distributions of anisotropy axes have been studied. Both are characterized by a parameter that allows control of the degree of disorder in the system. By using numerical simulations we analyze the hysteresis loop properties and characterize the statistical distribution of avalanches occuring during the metastable evolution of the system driven by an external field. A disorder-induced critical point is found in which the hysteresis loop changes from displaying a typical ferromagnetic magnetization jump to a rather smooth loop exhibiting only tiny avalanches. The critical point is characterized by a set of critical exponents, which are consistent with the universal values proposed from the study of other simpler models., Comment: 40 pages, 21 figures, Accepted for publication in Phys. Rev. B

We numerically study the dynamical properties of fully frustrated models in 2 and 3 dimensions. The results obtained support the hypothesis that the percolation transition of the Kasteleyn-Fortuin clusters corresponds to the onset of stretched exponential autocorrelation functions in systems without disorder. This dynamical behavior may be due to the ``large scale'' effects of frustration, present below the percolation threshold. Moreover these results are consistent with the picture suggested by Campbell et al. in space of configurations., Comment: 8 pages, 11 figures, revised version

We have studied the Potts spin glass with 2-state Ising spins and s-state Potts variables using a cluster Monte Carlo dynamics. The model recovers the +- J Ising spin glass (SG) for s=1 and exhibits for all s a SG transition at T_{SG}(s) and a percolation transition at higher temperature T_p(s). We have shown that for all values of $s\neq 1$ at T_p(s) there is a thermodynamical transition in the universality class of a ferromagnetic s-state Potts model. The efficiency of the cluster dynamics is compared with that of standard spin flip dynamics., 8 pages, Latex, with 8 EPS figs

By numerical simulations of the $3d$ Ising spin glass we find evidence that spontaneous replica symmetry breaking theory and not the droplet model describes with good accuracy the equilibrium behavior of the system., Comment: PHYSREV format, 2 .ps figures added with figure command in uufiles format

We study the relaxational dynamics of the one-spin facilitated Ising model introduced by Fredrickson and Andersen. We show the existence of a critical time which separates an initial regime in which the relaxation is exponentially fast and aging is absent from a regime in which relaxation becomes slow and aging effects are present. The presence of this fast exponential process and its associated critical time is in agreement with some recent experimental results on fragile glasses., 20 Pages + 7 Figures, Revtex

We study the behavior of the random-bond Ising model at zero temperature by numerical simulations for a variable amount of disorder. The model is an example of systems exhibiting a fluctuationless first-order phase transition similar to some field-induced phase transitions in ferromagnetic systems and the martensitic phase transition appearing in a number of metallic alloys. We focus on the study of the hysteresis cycles appearing when the external field is swept from positive to negative values. By using a finite-size scaling hypothesis, we analyze the disorder-induced phase transition between the phase exhibiting a discontinuity in the hysteresis cycle and the phase with the continuous hysteresis cycle. Critical exponents characterizing the transition are obtained. We also analyze the size and duration distributions of the magnetization jumps (avalanches).

The ferromagnetic Ising spin-(1/2 model in a finite simple-cubic lattice Λ is studied by Monte Carlo methods when two subsets of the lattice sites in Λ, say Ω + and Ω − , contain (the same number of) spins fixed at ±1, respectively, the global defect concentration being x≤0.25. We study the thermodynamic properties of the model for different choices of Ω= Ω + ∪ Ω − . A finite-size-scaling analysis reveals that the transition remains second order with pure critical exponents for regularly spaced defects, the critical temperature varying with the symmetry of Ω. Any small randomness in Ω, however, makes the transition weakly first order; the transition becomes more abrupt for defects located fully at random, and the long-range order is suppressed when the numbers of defects in Ω + and Ω − differ from each other. We also discuss our findings in relation to the random-field and frustration problems.

We study the phase diagram and other general macroscopic properties of an interacting spin (or particle) system out of equilibrium, namely, a reaction-diffusion Ising model whose time evolution occurs as a consequence of a combination of spin-flip (Glauber) and spin-exchange (Kawasaki) processes. The Glauber rate at site x when the configuration is s, say c(s;x), satisfies detailed balance at a reciprocal temperature β, while the Kawasaki rate for the interchange between nearest-neighbor sites x and y, Γc(s;x,y), satisfies detailed balance at temperature β’. We derive hydrodynamic-type macroscopic equations from the stochastic microscopic model for β’,β≥0 and large Γ when time and space are rescaled by Γ and √Γ , respectively, and study the homogeneous steady solutions of those equations when Γ→∞. We state some general theorems for β’=0 and solve explicitly the model with different choices c(s;x) for systems of arbitrary dimension d when β’=0 and also for d=1 when β’≠0. We also describe new Monte Carlo data for finite Γ, β’=0, and d=1,2. The latter suggests, in particular, the existence of phase transitions for d=1, finite Γ, and some choices for c(s;x).

We study steady states in d-dimensional lattice systems that evolve in time by a probabilistic majority rule, which corresponds to the zero-temperature limit of a system with conflicting dynamics. The rule satisfies detailed balance for d=1 but not for d>1. We find numerically nonequilibrium critical points of the Ising class for d=2 and 3.

A numerical study is presented of the third-dimensional Gaussian random-field Ising model at T50 driven by an external field. Standard synchronous relaxation dynamics is employed to obtain the magnetization versus field hysteresis loops. The focus is on the analysis of the number and size distribution of the magnetization avalanches. They are classified as being nonspanning, one-dimensional-spanning, two-dimensional-spanning, or three-dimensional-spanning depending on whether or not they span the whole lattice in different space directions. Moreover, finite-size scaling analysis enables identification of two different types of nonspanning avalanches ~critical and noncritical! and two different types of three-dimensional-spanning avalanches ~critical and subcritical!, whose numbers increase with L as a power law with different exponents. We conclude by giving a scenario for avalanche behavior in the thermodynamic limit.

A general scheme for devising efficient cluster dynamics proposed in a previous letter [Phys.Rev.Lett. 72, 1541 (1994)] is extensively discussed. In particular the strong connection among equilibrium properties of clusters and dynamic properties as the correlation time for magnetization is emphasized. The general scheme is applied to a number of frustrated spin model and the results discussed., 17 pages LaTeX + 16 figures; will appear in Phys. Rev. E

We analyze the stationary nonequilibrium state of a spin system evolving under combined flips at temperature β − 1 and exchanges at β=0. Computer simulations indicate that the phase transition changes, as the exchange rate Γ increases, from second to first order. We interpret this as a changeover from Ising behavior for small Γ to mean-field behavior for Γ→∞ where the magnetization is discontinuous in the ‘‘continuum limit.’’

The Invaded Cluster (IC) dynamics introduced by Machta et al. [Phys. Rev. Lett. 75 2792 (1995)] is extended to the fully frustrated Ising model on a square lattice. The properties of the dynamics which exhibits numerical evidence of self-organized criticality are studied. The fluctuations in the IC dynamics are shown to be intrinsic of the algorithm and the fluctuation-dissipation theorem is no more valid. The relaxation time is found very short and does not present critical size dependence., Comment: notes and refernences added, some minor changes in text and fig.3,5,7 16 pages, Latex, 8 EPS figures, submitted to Phys. Rev. E