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  "authors": [
    {
      "surname": "Schweitzer", 
      "given_names": "Dominik", 
      "affiliations": [
        {
          "country": "Germany", 
          "value": "Institut f\u00fcr Theoretische Physik, Justus-Liebig-Universit\u00e4t, Gie\u00dfen, Germany"
        }
      ], 
      "full_name": "Schweitzer, Dominik", 
      "orcid": "0000-0003-0303-9165", 
      "email": "dominik.schweitzer@theo.physik.uni-giessen.de"
    }, 
    {
      "surname": "Schlichting", 
      "given_names": "S\u00f6ren", 
      "affiliations": [
        {
          "country": "Germany", 
          "value": "Fakult\u00e4t f\u00fcr Physik, Universit\u00e4t Bielefeld, Bielefeld, Germany"
        }
      ], 
      "full_name": "Schlichting, S\u00f6ren", 
      "orcid": "0000-0003-3713-2325", 
      "email": "sschlichting@physik.uni-bielefeld.de"
    }, 
    {
      "affiliations": [
        {
          "country": "Germany", 
          "value": "Institut f\u00fcr Theoretische Physik, Justus-Liebig-Universit\u00e4t, Gie\u00dfen, Germany"
        }, 
        {
          "country": "Germany", 
          "value": "Helmholtz Research Academy Hessen for FAIR (HFHF), Gie\u00dfen, Germany"
        }
      ], 
      "surname": "von Smekal", 
      "email": "lorenz.smekal@physik.uni-giessen.de", 
      "full_name": "von Smekal, Lorenz", 
      "given_names": "Lorenz"
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  "titles": [
    {
      "source": "Elsevier", 
      "title": "Spectral functions and dynamic critical behavior of relativistic Theories"
    }
  ], 
  "collections": [
    {
      "primary": "Nuclear Physics B"
    }
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      "journal_volume": "960 C", 
      "journal_title": "Nuclear Physics B", 
      "material": "article", 
      "artid": "115165", 
      "year": 2020
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  "abstracts": [
    {
      "source": "Elsevier", 
      "value": "We investigate the dynamic critical behavior of a relativistic scalar field theory with <math><msub><mrow><mi>Z</mi></mrow><mrow><mn>2</mn></mrow></msub></math> symmetry by calculating spectral functions of the order parameter at zero and non-vanishing momenta from first-principles classical-statistical lattice simulations in real-time. We find that at temperatures above the critical point (<math><mi>T</mi><mo>&gt;</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>c</mi></mrow></msub></math>), the spectral functions are well described by relativistic quasi-particle peaks. Close to the transition temperature (<math><mi>T</mi><mo>\u223c</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>c</mi></mrow></msub></math>), we observe strong infrared contributions building up. In the ordered phase at low temperatures (<math><mi>T</mi><mo>&lt;</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>c</mi></mrow></msub></math>), in addition to the quasi-particle peak, we observe a soft mode with a dispersion relation indicative of collective excitations. Investigating the spectral functions close to <math><msub><mrow><mi>T</mi></mrow><mrow><mi>c</mi></mrow></msub></math>, we demonstrate that the behavior in the vicinity of the critical point is controlled by dynamic scaling functions and the dynamic critical exponent z, which we determine from our simulations. By considering the equations of motion for a closed system and a system coupled to a heat bath, we extract the dynamic critical behavior for two different dynamic universality classes (Models A &amp; C) in two and three spatial dimensions."
    }
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