Quenching to field-stabilized Adam Iaizzi* Postdoctoral Fellow - - PowerPoint PPT Presentation
J24.00013 Quenching to field-stabilized Adam Iaizzi* Postdoctoral Fellow magnetization plateaus in the National Taiwan University unfrustrated Ising antiferromagnet Better title: Stable frozen states without disorder
J24.00013
Adam Iaizzi* Postdoctoral Fellow National Taiwan University
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*iaizzi@bu.edu
Better title: Stable frozen states without disorder
Adam Iaizzi - iaizzi@bu.edu
❖ ❖ Square lattice ❖ Antiferromagnet ❖ 2-fold degenerate GS ❖ Tc = 2.26… ❖ Simplest model with PT ❖ With field: poorly studied
H = J∑
⟨i,j⟩
σiσj − h∑
i
σi
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1 2 3 4 5
h
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
m
Exact, T=0
m(T = 0, h) = ( h < 4 1 h > 4
Adam Iaizzi - iaizzi@bu.edu
❖ Metropolis Monte Carlo ❖ Single-spin-flip updates ❖ Choose spin at random ❖ Flip with probability ❖ Quench: ❖ Start from
(totally random) state
❖ Instant quench to ❖ What happens?
P = min [1,e−ΔE/T] T = ∞ T
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1 2 3 4 5
h
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
m
Exact, T=0
Adam Iaizzi - iaizzi@bu.edu
❖ Instantaneous quench to
finite T<Tc
❖ High T: EQ ❖ Low T: Non-ergodic ❖ Plateaus ❖ Stable frozen states ❖ No intrinsic disorder ❖ Valleys of ergodicity
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1 2 3 4 5
h
0.0 0.2 0.4 0.6 0.8 1.0
m
= 2 = 4 = 8 = 16 = 64
Adam Iaizzi - iaizzi@bu.edu
❖ Ergodic for ❖ From now on:
h = 0, ± 2, ± 4 T = 0
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1 2 3 4 5
h
0.0 0.2 0.4 0.6 0.8 1.0
m
= 2 = 4 = 8 = 16 = 64
m(T = 0, h) = 8 > > > > > > > < > > > > > > > : h = 0, 0.057 0 < h < 2J, h = 2J, 0.282 2J < h < 4J, 0.55 h = hs = 4J, 1 h > hs.
Adam Iaizzi - iaizzi@bu.edu
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Second plateau: h = 3
View animations online: http://bit.ly/iaizziTPS
Adam Iaizzi - iaizzi@bu.edu
❖ 10 local spin configurations ❖ 5 pairs
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+ + + + + + + _ + + + + + + + + + + + + + + + _ _ _ + + + _ _ _
h<2 h<4 h=0 h>0 h>2 h>4
x = +1 x = -1 y = +4 y = -4 y = -2 y = 0 y = +2
x =σi = ±1 y = X
j
σj = 0, ±2, ±4
P = min h 1, e(yh)∆x/T i
Adam Iaizzi - iaizzi@bu.edu
❖
dynamics:
❖ Accept if ❖ Reject if ❖
: reversible update
❖ Reversible updates when ❖ Valleys of ergodicity
T = 0 ΔE ≤ 0 ΔE > 0 ΔE = 0 h = y = 0, ± 2, ± 4
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+ + + + + + + _ + + + + + + + + + + + + + + + _ _ _ + + + _ _ _
h<2 h<4 h=0 h>0 h>2 h>4
x = +1 x = -1 y = +4 y = -4 y = -2 y = 0 y = +2
Adam Iaizzi - iaizzi@bu.edu
❖ Maps onto ferromagnet ❖ Bulk domains and straight
domain walls stable
❖
quench, stuck in stripe state w/
❖ Connection to critical
percolation theory
❖ Otherwise reach G.S.
T = 0 P = 0.3390...
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Spirin, Krapivsky, Redner, PRE 65 016119 (2001)
nonzero temperature: a nucleation of a dent freely flippable spins are indicated; b diffusive growth of the dent; c dent reaches the system size and hence the domain wall steps to the left. This overall process ultimately leads to the disappearance of the stripe.
Barros, Krapivsky, Redner, PRE 80 040101(R) (2009)
Adam Iaizzi - iaizzi@bu.edu
❖ ❖ Corner domain walls now
stable
❖ Corners host excess + spin ❖ Net magnetization 0.057
0 < h < 2J
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Adam Iaizzi - iaizzi@bu.edu
❖ Straight line DW not stable ❖ Corners/diagonal DW stable ❖ Excess + spin along DW ❖ Net magnetization 0.282
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Adam Iaizzi - iaizzi@bu.edu
❖ Does not freeze ❖ Vanishing dependence ❖ Coexistence of ❖ 2x AFM G.S. ❖ Fully-polarized state ❖ Equivalent to hard-squares
problem
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1 2 3 4 5
h
0.0 0.2 0.4 0.6 0.8 1.0
m
= 2 = 4 = 8 = 16 = 64
❖ Instantaneous quenches in Ising AFM + field ❖ Stable plateaus without disorder ❖ In plateau: all spins unflippable ❖ Describe in terms of stable local configurations ❖ Ergodicity restored when
updates available
❖ Useful for understanding when MC fails ❖ Monte Carlo dynamics physical dynamics ❖ We choose the dynamics ❖ Plateau states are local energy minima under these dynamics ❖ Choosing dynamics rearranges energy surface
ΔE = 0 ≠
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❖ Enumerate plateau states? ❖ Connect to percolation theory? ❖ Derive magnetization in plateaus ❖ What is the finite-T scaling of “valleys of ergodicity”? ❖ Other lattices? ❖ Other dynamics?
Adam Iaizzi email: iaizzi@bu.edu web: www.iaizzi.me
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Preprint available: arXiv:2001.09268