Skip to main content
We gratefully acknowledge support from the Simons Foundation, member institutions, and all contributors. Donate
arXiv logo
Cornell University Logo

Mathematical Physics

arXiv:1811.04386 (math-ph)
[Submitted on 11 Nov 2018 (v1), last revised 15 Jun 2019 (this version, v3)]

Title:Zero-variance of perturbation Hamiltonian density in perturbed spin systems

Authors:C. Itoi
View PDF
Abstract:We study effects of perturbation Hamiltonian to quantum spin systems which can include quenched disorder. Model-independent inequalities are derived, using an additional artificial disordered perturbation. These inequalities enable us to prove that the variance of the perturbation Hamiltonian density vanishes in the infinite volume limit even if the artificial perturbation is switched off. This theorem is applied to spontaneous symmetry breaking phenomena in a disordered classical spin model, a quantum spin model without disorder and a disordered quantum spin model.
Comments: 15 pages, final version
Subjects: Mathematical Physics (math-ph); Statistical Mechanics (cond-mat.stat-mech); Quantum Physics (quant-ph)
MSC classes: 82B10, 82B26, 82B27, 82B44
Cite as: arXiv:1811.04386 [math-ph]
  (or arXiv:1811.04386v3 [math-ph] for this version)
  https://doi.org/10.48550/arXiv.1811.04386
Journal reference: J.Stat.Phys.176,556-573(2019)
Related DOI: https://doi.org/10.1007/s10955-019-02311-6

Submission history

From: Chigak Itoi [view email]
[v1] Sun, 11 Nov 2018 10:28:02 UTC (15 KB)
[v2] Sun, 3 Feb 2019 13:15:20 UTC (16 KB)
[v3] Sat, 15 Jun 2019 01:40:54 UTC (16 KB)
Full-text links:

Access Paper:

view license
Current browse context:
cond-mat.stat-mech
< prev   |   next >
new | recent | 2018-11
Change to browse by:
cond-mat
math
math-ph
math.MP
quant-ph

References & Citations

export BibTeX citation

Bookmark

BibSonomy logo Reddit logo

Bibliographic and Citation Tools

Bibliographic Explorer (What is the Explorer?)
Connected Papers (What is Connected Papers?)
Litmaps (What is Litmaps?)
scite Smart Citations (What are Smart Citations?)

Code, Data and Media Associated with this Article

alphaXiv (What is alphaXiv?)
CatalyzeX Code Finder for Papers (What is CatalyzeX?)
DagsHub (What is DagsHub?)
Gotit.pub (What is GotitPub?)
Hugging Face (What is Huggingface?)
Papers with Code (What is Papers with Code?)
ScienceCast (What is ScienceCast?)

Demos

Replicate (What is Replicate?)
Hugging Face Spaces (What is Spaces?)
TXYZ.AI (What is TXYZ.AI?)

Recommenders and Search Tools

Influence Flower (What are Influence Flowers?)
CORE Recommender (What is CORE?)

arXivLabs: experimental projects with community collaborators

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.

Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)