Communications in Mathematical Physics

, Volume 181, Issue 2, pp 409–446

Low temperature phase diagrams for quantum perturbations of classical spin systems

  • C. Borgs
  • R. Kotecký
  • D. Ueltschi


We consider a quantum spin system with Hamiltonian
$$H = H^{(0)} + \lambda V,$$
whereH(0) is diagonal in a basis ∣s〉=⊗xsx〉 which may be labeled by the configurationss={sx} of a suitable classical spin system on ℤd,
$$H^{(0)} |s\rangle = H^{(0)} (s)|s\rangle .$$
We assume thatH(0)(s) is a finite range Hamiltonian with finitely many ground states and a suitable Peierls condition for excitation, whileV is a finite range or exponentially decaying quantum perturbation. Mapping thed dimensional quantum system onto aclassical contour system on ad+1 dimensional lattice, we use standard Pirogov-Sinai theory to show that the low temperature phase diagram of the quantum spin system is a small perturbation of the zero temperature phase diagram of the classical HamiltonianH(0), provided λ is sufficiently small. Our method can be applied to bosonic systems without substantial change. The extension to fermionic systems will be discussed in a subsequent paper.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer-Verlag 1996

Authors and Affiliations

  • C. Borgs
    • 1
  • R. Kotecký
    • 2
  • D. Ueltschi
    • 3
  1. 1.School of MathematicsInstitute for Advanced StudyPrincetonUSA
  2. 2.Centre de Physique ThéoriqueCNRSMarseilleFrance
  3. 3.Institut de Physique ThéoriqueEPFLausanneSwitzerland
  4. 4.Institut für Theoretische PhysikFreie Universität BerlinBerlinDeutschland
  5. 5.Center for Theoretical StudyCharles UniversityPraha

Personalised recommendations