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Papers by Rogelio Diaz-Mendez

Research paper thumbnail of Glass Transitions in Monodisperse Cluster-Forming Ensembles: Vortex Matter in Type-1.5 Superconductors

Physical Review Letters, 2017

Research paper thumbnail of Is a Good Offensive Always the Best Defense?

International Game Theory Review, 2016

A checkers-like model game with a simplified set of rules is studied through extensive simulation... more A checkers-like model game with a simplified set of rules is studied through extensive simulations of agents with different expertise and strategies. The introduction of complementary strategies, in a quite general way, provides a tool to mimic the basic ingredients of a wide scope of real games. We find that only for the player having the higher offensive expertise (the dominant player), maximizing the offensive always increases the probability to win. For the nondominant player, interestingly, a complete minimization of the offensive becomes the best way to win in many situations, depending on the relative values of the defense expertise. Further simulations on the interplay of defense expertise were done separately, in the context of a fully offensive scenario, offering a starting point for analytical treatments. In particular, we established that in this scenario the total number of moves is defined only by the player with the lower defensive expertise. We believe that these res...

Research paper thumbnail of Monodisperse cluster crystals: Classical and quantum dynamics

Research paper thumbnail of Solving the one-dimensional Ising chain via mathematical induction: An intuitive approach to the transfer matrix

European Journal of Physics

Research paper thumbnail of The frustrated spherical model: an alternative to Ginzburg-Landau Hamiltonians with competing interactions

Arxiv preprint arXiv:1012.4780, 2010

Abstract: We solve analytically the Langevin dynamics of the classic spherical model considering ... more Abstract: We solve analytically the Langevin dynamics of the classic spherical model considering the ferromagnetic exchange and a long-range antiferromagnetic interaction. Our results in the asymptotic regime, shows an equivalence in the functionality of the spatial ...

Research paper thumbnail of Dynamics of systems with isotropic competing interactions in an external field: a Langevin approach

The European Physical Journal B, 2011

We study the Langevin dynamics of a ferromagnetic Ginzburg-Landau Hamiltonian with a competing lo... more We study the Langevin dynamics of a ferromagnetic Ginzburg-Landau Hamiltonian with a competing long-range repulsive term in the presence of an external magnetic field. The model is analytically solved within the self consistent Hartree approximation for two different initial conditions: disordered or zero field cooled (ZFC), and fully magnetized or field cooled (FC). To test the predictions of the approximation we develop a suitable numerical scheme to ensure the isotropic nature of the interactions. Both the analytical approach and the numerical simulations of two-dimensional finite systems confirm a simple aging scenario at zero temperature and zero field. At zero temperature a critical field hc is found below which the initial conditions are relevant for the long time dynamics of the system. For h < hc a logarithmic growth of modulated domains is found in the numerical simulations but this behavior is not captured by the analytical approach which predicts a t 1/2 growth law at T = 0.

Research paper thumbnail of Non-Arrhenius relaxation of the Heisenberg model with dipolar and anisotropic interactions

Journal of Magnetism and Magnetic Materials, 2012

The dynamical properties of a 2D Heisenberg model with dipolar interactions and perpendicular ani... more The dynamical properties of a 2D Heisenberg model with dipolar interactions and perpendicular anisotropy are studied using Monte Carlo simulations in two different ordered regions of the equilibrium phase diagram. We find a temperature defining a dynamical transition below which the relaxation suddenly slows down and the system aparts from the typical Arrhenius relaxation to a Vogel-Fulcher-Tamann law. This anomalous behavior is observed in the scaling of the magnetic relaxation and may eventually lead to a freezing of the system. Through the analysis of the domain structures we explain this behavior in terms of the domains dynamics. Moreover, we calculate the energy barriers distribution obtained from the data of the magnetic viscosity. Its shape supports our comprehension of both, the Vogel-Fulcher-Tamann dynamical slowing down and the freezing mechanism.

Research paper thumbnail of Loss of relaxor properties due to dipolar interactions in ferroelectrics: A 2D Monte Carlo study

physica status solidi (b), 2012

Phone: The behavior of the dielectric response in relaxor ferroelectric materials is studied by m... more Phone: The behavior of the dielectric response in relaxor ferroelectric materials is studied by means of Monte Carlo simulations of a simple two-dimensional (2D) generic model. It is showed that the shifting with the frequency of the peak of the temperature dependence of the dielectric permittivity e can be obtained just by considering a randomly distributed pinning anisotropy for the out-plane projection of the polar nanoregions. It is also showed that the consideration of a weak long-range dipolar interaction between nanodomains continuously drives the system to a non-relaxor ferroelectric state in which a single peak is observed for the dielectric permittivity.

Research paper thumbnail of H-T phase diagram of the two-dimensional Ising model with exchange and dipolar interactions

Physical Review B, 2010

We explore the equilibrium properties of a two-dimensional Ising spin model with short-range exch... more We explore the equilibrium properties of a two-dimensional Ising spin model with short-range exchange and long-range dipolar interactions as a function of the applied magnetic field H. The model is studied through extensive Monte Carlo simulations that show the existence of many modulated phases with long range orientational order for a wide range of fields. These phases are characterized by different wave vectors that change discontinuously with the magnetic field. We provide numerical evidence supporting the existence of first order transitions between these phases. At higher fields our results suggest a Kosterliz-Thouless scenario for the transition from a bubble to a ferromagnetic phase.

Research paper thumbnail of Monte Carlo simulations of the equilibrium and non-equilibrium properties of low-dimensional magnetic systems with long-range dipolar interactions

Journal of Magnetism and Magnetic Materials, 2005

The equilibrium and non-equilibrium properties of a two-dimensional Ising-like spin system with b... more The equilibrium and non-equilibrium properties of a two-dimensional Ising-like spin system with both ferromagnetic exchange and long-range dipolar interactions are studied. Implementing the Ewald Sums (ES) for the calculation of the dipolar interaction we reproduced the results of the literature concerning the equilibrium-phase diagram and the stability of the phases. We also investigated the aging regime and the Fluctuation–Dissipation Theorem

Research paper thumbnail of Symmetry breaking in frustrated systems: effective fluctuation spectrum due to coupling effects

Arxiv preprint arXiv: …, 2010

Alejandro Mendoza-Coto,1,2 Rogelio Díaz-Méndez,3,2 Roberto Mulet,1, 2 Lucas Nicolao,4 and Daniel ... more Alejandro Mendoza-Coto,1,2 Rogelio Díaz-Méndez,3,2 Roberto Mulet,1, 2 Lucas Nicolao,4 and Daniel A. Stariolo5 1Department of Theoretical Physics, Physics Faculty, University of Havana, La Habana, CP 10400, Cuba 2“Henri-Poincaré-Group” of Complex Systems, ...

Research paper thumbnail of Glass Transitions in Monodisperse Cluster-Forming Ensembles: Vortex Matter in Type-1.5 Superconductors

Physical Review Letters, 2017

Research paper thumbnail of Is a Good Offensive Always the Best Defense?

International Game Theory Review, 2016

A checkers-like model game with a simplified set of rules is studied through extensive simulation... more A checkers-like model game with a simplified set of rules is studied through extensive simulations of agents with different expertise and strategies. The introduction of complementary strategies, in a quite general way, provides a tool to mimic the basic ingredients of a wide scope of real games. We find that only for the player having the higher offensive expertise (the dominant player), maximizing the offensive always increases the probability to win. For the nondominant player, interestingly, a complete minimization of the offensive becomes the best way to win in many situations, depending on the relative values of the defense expertise. Further simulations on the interplay of defense expertise were done separately, in the context of a fully offensive scenario, offering a starting point for analytical treatments. In particular, we established that in this scenario the total number of moves is defined only by the player with the lower defensive expertise. We believe that these res...

Research paper thumbnail of Monodisperse cluster crystals: Classical and quantum dynamics

Research paper thumbnail of Solving the one-dimensional Ising chain via mathematical induction: An intuitive approach to the transfer matrix

European Journal of Physics

Research paper thumbnail of The frustrated spherical model: an alternative to Ginzburg-Landau Hamiltonians with competing interactions

Arxiv preprint arXiv:1012.4780, 2010

Abstract: We solve analytically the Langevin dynamics of the classic spherical model considering ... more Abstract: We solve analytically the Langevin dynamics of the classic spherical model considering the ferromagnetic exchange and a long-range antiferromagnetic interaction. Our results in the asymptotic regime, shows an equivalence in the functionality of the spatial ...

Research paper thumbnail of Dynamics of systems with isotropic competing interactions in an external field: a Langevin approach

The European Physical Journal B, 2011

We study the Langevin dynamics of a ferromagnetic Ginzburg-Landau Hamiltonian with a competing lo... more We study the Langevin dynamics of a ferromagnetic Ginzburg-Landau Hamiltonian with a competing long-range repulsive term in the presence of an external magnetic field. The model is analytically solved within the self consistent Hartree approximation for two different initial conditions: disordered or zero field cooled (ZFC), and fully magnetized or field cooled (FC). To test the predictions of the approximation we develop a suitable numerical scheme to ensure the isotropic nature of the interactions. Both the analytical approach and the numerical simulations of two-dimensional finite systems confirm a simple aging scenario at zero temperature and zero field. At zero temperature a critical field hc is found below which the initial conditions are relevant for the long time dynamics of the system. For h < hc a logarithmic growth of modulated domains is found in the numerical simulations but this behavior is not captured by the analytical approach which predicts a t 1/2 growth law at T = 0.

Research paper thumbnail of Non-Arrhenius relaxation of the Heisenberg model with dipolar and anisotropic interactions

Journal of Magnetism and Magnetic Materials, 2012

The dynamical properties of a 2D Heisenberg model with dipolar interactions and perpendicular ani... more The dynamical properties of a 2D Heisenberg model with dipolar interactions and perpendicular anisotropy are studied using Monte Carlo simulations in two different ordered regions of the equilibrium phase diagram. We find a temperature defining a dynamical transition below which the relaxation suddenly slows down and the system aparts from the typical Arrhenius relaxation to a Vogel-Fulcher-Tamann law. This anomalous behavior is observed in the scaling of the magnetic relaxation and may eventually lead to a freezing of the system. Through the analysis of the domain structures we explain this behavior in terms of the domains dynamics. Moreover, we calculate the energy barriers distribution obtained from the data of the magnetic viscosity. Its shape supports our comprehension of both, the Vogel-Fulcher-Tamann dynamical slowing down and the freezing mechanism.

Research paper thumbnail of Loss of relaxor properties due to dipolar interactions in ferroelectrics: A 2D Monte Carlo study

physica status solidi (b), 2012

Phone: The behavior of the dielectric response in relaxor ferroelectric materials is studied by m... more Phone: The behavior of the dielectric response in relaxor ferroelectric materials is studied by means of Monte Carlo simulations of a simple two-dimensional (2D) generic model. It is showed that the shifting with the frequency of the peak of the temperature dependence of the dielectric permittivity e can be obtained just by considering a randomly distributed pinning anisotropy for the out-plane projection of the polar nanoregions. It is also showed that the consideration of a weak long-range dipolar interaction between nanodomains continuously drives the system to a non-relaxor ferroelectric state in which a single peak is observed for the dielectric permittivity.

Research paper thumbnail of H-T phase diagram of the two-dimensional Ising model with exchange and dipolar interactions

Physical Review B, 2010

We explore the equilibrium properties of a two-dimensional Ising spin model with short-range exch... more We explore the equilibrium properties of a two-dimensional Ising spin model with short-range exchange and long-range dipolar interactions as a function of the applied magnetic field H. The model is studied through extensive Monte Carlo simulations that show the existence of many modulated phases with long range orientational order for a wide range of fields. These phases are characterized by different wave vectors that change discontinuously with the magnetic field. We provide numerical evidence supporting the existence of first order transitions between these phases. At higher fields our results suggest a Kosterliz-Thouless scenario for the transition from a bubble to a ferromagnetic phase.

Research paper thumbnail of Monte Carlo simulations of the equilibrium and non-equilibrium properties of low-dimensional magnetic systems with long-range dipolar interactions

Journal of Magnetism and Magnetic Materials, 2005

The equilibrium and non-equilibrium properties of a two-dimensional Ising-like spin system with b... more The equilibrium and non-equilibrium properties of a two-dimensional Ising-like spin system with both ferromagnetic exchange and long-range dipolar interactions are studied. Implementing the Ewald Sums (ES) for the calculation of the dipolar interaction we reproduced the results of the literature concerning the equilibrium-phase diagram and the stability of the phases. We also investigated the aging regime and the Fluctuation–Dissipation Theorem

Research paper thumbnail of Symmetry breaking in frustrated systems: effective fluctuation spectrum due to coupling effects

Arxiv preprint arXiv: …, 2010

Alejandro Mendoza-Coto,1,2 Rogelio Díaz-Méndez,3,2 Roberto Mulet,1, 2 Lucas Nicolao,4 and Daniel ... more Alejandro Mendoza-Coto,1,2 Rogelio Díaz-Méndez,3,2 Roberto Mulet,1, 2 Lucas Nicolao,4 and Daniel A. Stariolo5 1Department of Theoretical Physics, Physics Faculty, University of Havana, La Habana, CP 10400, Cuba 2“Henri-Poincaré-Group” of Complex Systems, ...