TY - JOUR
T1 - On spin systems with quenched randomness
T2 - Classical and quantum
AU - Greenblatt, Rafael L.
AU - Aizenman, Michael
AU - Lebowitz, Joel L.
N1 - Funding Information:
The first author’s work was supported by NSF Grant DMR-044-2066 and AFOSR Grant AF-FA9550-04, the second author’s work was supported by NSF Grant DMS-060-2360 and the third author’s work was supported by NSF Grant DMR-044-2066 and AFOSR Grant AF-FA9550-04.
PY - 2010/8/1
Y1 - 2010/8/1
N2 - The rounding of first-order phase transitions by quenched randomness is stated in a form which is applicable to both classical and quantum systems: The free energy, as well as the ground state energy, of a spin system on a d-dimensional lattice is continuously differentiable with respect to any parameter in the Hamiltonian to which some randomness has been added when d ≤ 2. This implies absence of jumps in the associated order parameter, e.g., the magnetization in the case of a random magnetic field. A similar result applies in cases of continuous symmetry breaking for d ≤ 4. Some questions concerning the behavior of related order parameters in such random systems are discussed.
AB - The rounding of first-order phase transitions by quenched randomness is stated in a form which is applicable to both classical and quantum systems: The free energy, as well as the ground state energy, of a spin system on a d-dimensional lattice is continuously differentiable with respect to any parameter in the Hamiltonian to which some randomness has been added when d ≤ 2. This implies absence of jumps in the associated order parameter, e.g., the magnetization in the case of a random magnetic field. A similar result applies in cases of continuous symmetry breaking for d ≤ 4. Some questions concerning the behavior of related order parameters in such random systems are discussed.
KW - Lattice spin systems
KW - Quenched disorder
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U2 - 10.1016/j.physa.2009.12.066
DO - 10.1016/j.physa.2009.12.066
M3 - Article
AN - SCOPUS:79960968277
VL - 389
SP - 2902
EP - 2906
JO - Physica A: Statistical Mechanics and its Applications
JF - Physica A: Statistical Mechanics and its Applications
SN - 0378-4371
IS - 15
ER -