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

UR - http://www.scopus.com/inward/record.url?scp=79960968277&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79960968277&partnerID=8YFLogxK

U2 - 10.1016/j.physa.2009.12.066

DO - 10.1016/j.physa.2009.12.066

M3 - Article

AN - SCOPUS:79960968277

SN - 0378-4371

VL - 389

SP - 2902

EP - 2906

JO - Physica A: Statistical Mechanics and its Applications

JF - Physica A: Statistical Mechanics and its Applications

IS - 15

ER -