{
  "id": "1701.06164",
  "version": "v1",
  "published": "2017-01-22T13:44:35.000Z",
  "updated": "2017-01-22T13:44:35.000Z",
  "title": "Glauber's Ising chain between two thermostats",
  "authors": [
    "F. Cornu",
    "H. J. Hilhorst"
  ],
  "comment": "43 pages",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "We consider a one-dimensional Ising model each of whose $N$ spins is in contact with two thermostats of distinct temperatures $T_1$ and $T_2$. Under Glauber dynamics the stationary state happens to coincide with the equilibrium state at an effective intermediate temperature $T(T_1,T_2)$. The system nevertheless carries a nontrivial energy current between the thermostats. By means of the fermionization technique, for a chain initially in equilibrium at an arbitrary temperature $T_0$ we calculate the Fourier transform of the probability $P({\\cal Q};\\tau)$ for the time-integrated energy current ${\\cal Q}$ during a finite time interval $\\tau$. In the long time limit we determine the corresponding generating function for the cumulants per site and unit of time $\\langle{\\cal Q}^n\\rangle_{\\rm c}/(N\\tau)$ and explicitly give those with $n=1,2,3,4.$ We exhibit various phenomena in specific regimes: kinetic mean-field effects when one thermostat flips any spin less often than the other one, as well as dissipation towards a thermostat at zero temperature. Moreover, when the system size $N$ goes to infinity while the effective temperature $T$ vanishes, the cumulants of ${\\cal Q}$ per unit of time grow linearly with $N$ and are equal to those of a random walk process. In two adequate scaling regimes involving $T$ and $N$ we exhibit the dependence of the first correction upon the ratio of the spin-spin correlation length $\\xi(T)$ and the size $N$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-01-22T13:44:35.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "glaubers ising chain",
      "thermostat",
      "finite time interval",
      "nontrivial energy current",
      "stationary state happens"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 43,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}