Convergence and Critical Phenomena Studies in \(\phi_{1+1}^{4}\) -Field Theories via the Coupled Cluster Method

  • H. Kümmel
Part of the Recent Progress in Many-Body Theories book series (RPMT, volume 1)


During the last few years we have explored the feasibility of many body methods, especially the coupled cluster method (CCM) 1–7 in quantum field theory. The main objects were the various φ4 field theories in one space and one time dimension. In general, CCM was quite successful - with one important exception: due to Simon and Griffith 8 we know that there is a critical point corresponding to a second order phase transition. Clearly this implies infinite correlation length - and a breakdown of most if not all approximation methods. Therefore we found convergence problems around the critical point, originally both in the so called symmetry breaking as well as in the symmetrical Hamiltonian. I have reported on this at the last many body conference9.


Symmetry Breaking Critical Region Order Phase Transition Particle State Lorentz Invariance 
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Copyright information

© Plenum Press, New York 1988

Authors and Affiliations

  • H. Kümmel
    • 1
  1. 1.Institut für Theoretische Physik IIRuhr-Universität BochumBochum 1West Germany

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