Dynamical temperature for spin systems

Nurdin, Wira Bahari; Schotte, K. D.

doi:10.1103/physreve.61.3579

Cited by 37 publications

(27 citation statements)

References 8 publications

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“…The initial state for the time integration was generated from the procedure described in Sec. II C. The spin temperature was measured using the formula developed by Nurdin et al [53].…”

Section: Simulation Detailsmentioning

confidence: 99%

Collective dynamics in atomistic models with coupled translational and spin degrees of freedom

et al. 2017

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Using an atomistic model that simultaneously treats the dynamics of translational and spin degrees of freedom, we perform combined molecular and spin dynamics simulations to investigate the mutual influence of the phonons and magnons on their respective frequency spectra and lifetimes in ferromagnetic bcc iron. By calculating the Fourier transforms of the space-and time-displaced correlation functions, the characteristic frequencies and the linewidths of the vibrational and magnetic excitation modes were determined. Comparison of the results with that of the standalone molecular dynamics and spin dynamics simulations reveal that the dynamic interplay between the phonons and magnons leads to a shift in the respective frequency spectra and a decrease in the lifetimes. Moreover, in the presence of lattice vibrations, additional longitudinal magnetic excitations were observed with the same frequencies as the longitudinal phonons.

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“…The initial state for the time integration was generated from the procedure described in Sec. II C. The spin temperature was measured using the formula developed by Nurdin et al [53].…”

Section: Simulation Detailsmentioning

confidence: 99%

Collective dynamics in atomistic models with coupled translational and spin degrees of freedom

et al. 2017

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“…Instead of three components for the classical Heisenberg system in our preliminary paper [3], here we want to study the simpler XY -spin system where only two components S = S 1 , S 2 have to be taken into account, that is the spin vector is confined to a circle with radius S. No dynamical equation can be written down similar to ∂ S ∂t = S × H for the three dimensional vector S in a magnetic field H. The energy − H · S = −H S cos ϕ is the same for the two directions ±ϕ the vector S can point. Contrary to the three dimensional case, there is no continuous path between these equal energy states at ±ϕ.…”

Section: A General Approachmentioning

confidence: 99%

“…Although the energy is conserved one can determine the temperature for a system consisting of kinetic and potential energy the temperature by the average kinetic energy. With the recent advance in the understanding of the micro-canonical temperature initiated by Rugh [1][2][3], one can "measure" the temperature and also the specific heat along the trajectory of spin systems where such a decomposition of the energy does not exist. In the case of XY-spins one could also add the sum over the angular velocities but a dynamical check of statistical mechanics by a common molecular dynamics simulation is not an easy numerical task [4].…”

Section: Introductionmentioning

confidence: 99%

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Dynamical temperature study for classical planar spin systems

Nurdin

Schotte

2002

Physica A: Statistical Mechanics and its Applications

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Making use of the Rugh's micro-canonical approach to temperature we study XY-spin systems by the strictly energy conserving over-relaxation algorithm. In this micro-canonical simulation the temperature and also the specific heat are determined as averages of expressions easy to implement. The XY-chain is studied for a test. The second order transition on a cubic lattice and the first order transition on fcc lattice are analyzed in greater detail to have a more severe test about the feasibility of this micro-canonical method.

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“…Considering the square of this function one may in addition consider fluctuations of the inverse temperature. In case the ergodic hypothesis holds such averages may then be written as time averages using the dynamics of the classical Hamilton function (see, e.g., [67,68,5,60]). An important feature of a microcanonical ensemble is that the temperature may decrease with energy giving rise to a negative heat capacity.…”

Section: Introductionmentioning

confidence: 99%

Statistical ensembles and density of states

Kostrykin¹,

Schrader²

2002

Mathematical Results in Quantum Mechanics

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ABSTRACT. We propose a definition of microcanonical and canonical statistical ensembles based on the concept of density of states. This definition applies both to the classical and the quantum case. For the microcanonical case this allows for a definition of a temperature and its fluctuation, which might be useful in the theory of mesoscopic systems. In the quantum case the concept of density of states applies to one-particle Schrödinger operators, in particular to operators with a periodic potential or to random Anderson type models. In the case of periodic potentials we show that for the resulting n-particle system the density of states is [(n − 1)/2] times differentiable, such that like for classical microcanonical ensembles a (positive) temperature may be defined whenever n ≥ 5. We expect that a similar result should also hold for Anderson type models. We also provide the first terms in asymptotic expansions of thermodynamic quantities at large energies for the microcanonical ensemble and at large temperatures for the canonical ensemble. A comparison shows that then both formulations asymptotically give the same results.

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Dynamical temperature for spin systems

Abstract: A transcription of Rugh's geometrical approach to temperature is given for classical Heisenberg spin systems. For the simple case of a paramagnet with small and large numbers of spins we verify the approach. A numerical check for long spin chains using spin dynamics shows its practicality.

Cited by 37 publications

References 8 publications

Collective dynamics in atomistic models with coupled translational and spin degrees of freedom

Collective dynamics in atomistic models with coupled translational and spin degrees of freedom

Dynamical temperature study for classical planar spin systems

Statistical ensembles and density of states

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