solid-on-solid models with domain walls and a reflecting end out - - PowerPoint PPT Presentation

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solid-on-solid models with domain walls and a reflecting end out - - PowerPoint PPT Presentation

Nov 28, 2022 153 likes •274 views

Functional equations for solid-on-solid models with domain walls and a reflecting end out soon arXiv:1510.00xxx [math-ph] Jules La Lamers Institute for Theoretical Physics Utrecht University PhD thesis advisor: Prof dr Gleb Arutyunov

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Functional equations for

solid-on-solid models

with domain walls and a reflecting end

Jules La Lamers Institute for Theoretical Physics Utrecht University

DESY theory workshop Physics at the LHC and beyond 30 September 2015

  • ut soon arXiv:1510.00xxx [math-ph]

PhD thesis advisor: Prof dr Gleb Arutyunov (DESY)

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  • Ultimate goal for statistical-physical model:

compute

  • i. Study model for arbitrary finite size
  • ii. Take thermodynamic limit
  • Suprising fact: thermodynamics can be

sensitive to choice of boundary conditions!

Invitation

Boundary conditions in statistical physics

[Korepin Zinn-Justin '00] Jules Lamers

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  • Case study: solid-on-solid model

with domain walls and a reflecting end

  • Our goal: compute , for

Prior status: determinant formula

  • Results

ts

– Functional equation for the partition function – Solution, which is unique up to normalization,

gives new (multiple-integral) expression for

Outline

[Filali '11] Jules Lamers

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Solid-on-solid models

  • Growth of (bcc) crystals
  • Square 2d lattice with height variables at sites
  • Height difference between neighbours = 1

[Baxter '72] Jules Lamers

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Specific model

solid-on-solid with domain walls and a reflecting end

  • Solid-on-solid model on lattice
  • Boundary conditions:

domain walls (fixed heights)

[Korepin '82]

“reflection”

[Sklyanin '88] Jules Lamers

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Algebraic reformulation

diagrammatics for partition function

Jules Lamers

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SLIDE 7

Algebraic reformulation

partition function as an L-point correlator

“spectral parameters” Jules Lamers

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SLIDE 8

Algebraic reformulation

dynamical reflection algebra

  • generates,

together with operators , , , , the dynamical reflection algebra

– Various relations

e.g.

[Gervais Neveu '84] [Sklyanin '88] [Felder '95]

ratios of higher-order (Jacobi) theta functions in 's

commute commute & exchange 's commute & turn into Jules Lamers

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  • Algebraic-functional method

– Start from – Insert via – Move past all 's using e.g.

  • Result: functional equation for

[JL '15] [Galleas '08 '10]

Functional equation

Jules Lamers

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Results

1) Functional equation for partition function 2) Characterizes up to normalization factor 3) Solution: multiple-integral formula

[JL '15] Jules Lamers

polynomial in : odd Jacobi theta function

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  • Solid-on-solid model

with domain walls and a reflecting end

  • Results

ts

– Functional equation – Multiple-integral formula

  • Outl

tlook

– Thermodynamic limit – Comparison with other boundary conditions

Summary and beyond

  • ut soon arXiv:1510.00xxx [math-ph]

Jules Lamers