----------------------------------------------------------------
To read:

* Buffet and Pule; BU07/U07 relevant parts.
* HK paper
! BU08 paper

----------------------------------------------------------------
Current-semester plans:

Vzw:
* Vzw interactions ...
* rm p's from px, py, etc.
! special-case vzw for wormhole point ...

Worm Q's:
* gamma affects autocorr time via spa?
* diameter of close ball is fixed for beta; vanishingly small fraction
  of the volume for larger L?  Histogram of closure stats?
* Plot CPU-time scaling as f(N) for GK & worm; explain in a-priori terms.
* Animations ... :)
* Include the wormhole point in ell-cycles?
* Explain the difference between the f_S and f_I critical exponents.
  Put up plots, but also explain theoretically.
* Find the paper which discusses n_0 as well as rho_S.
* Replace cut1/cut2 w/ parameterized spec. number of HS/TS per closure attempt?
* metro stats per move type

For Thursday:
* Explain worm algorithm
  - for PIMC how much explanation?
  - for RCM  how much explanation?
  - fbb_pimc slides ...
  ! read the two papers.
* Explain finite-size scaling:
  ! Different nu?!?  (What ref? PR92 p. 3 left, NL04 p. 3 left)
    VA for simple f_S ~ t^nu.
  - Whisker plots
  - Why does VA trick on asymptotic whisker plots work?
  ! What is the true exponent?  (See PGP.)  Can it be determined somehow?
    Or can we use the VA trick to circumvent the problem?
* Describe what is still eluding me.
* Look at various new1.pdf, new2.pdf, fbb_pimc ...
* TASW03.pdf ...

>> merge pmt.c & point.c ...

Documentation:
!! log of completed runs!
* mhc
* Rename tca fig files & labels in disbody.
* Prove merge/split correctness for N_ell algorithm.
! Prove DB for pi MCMC ...
* "Constant of motion":  prove invariance of winding # in PBC case w/o cycrev.
* r_ell is #cycles of length ell; N_ell is #sites in cycles of length ell.
  I.e. N_ell = ell r_ell.  Illustrate this first by example.
  - Ceperley Rev. Mod. Phys. 67 279?
* bibents for all papers currently in my notebook

Analysis:
* replace n2fit.py & n2fit2.py with new logic ...
* colprint -l etc. into taskutil.
* os.mkdir() -- w/ -p, if possible.  Or wrapper.
!! linreg the new d^1/L way !!
  - Take L->infty pointwise and then try a power-law fit.
  - extrapolate to neg above T_c -- OK or not?
! catalog info about 1st/2nd-order phz xitns.
  - Original Ehrenfest:  lowest derivative of free energy which is discts @ Tc
    > Density = d free energy / d chemical potential
  - Current:
    > 1o has latent heat & mixed-phase regimes.
	> 2o are continuous phase transitions
	  Critical exponents and universality classes.
  - Huang and Wikipedia:  BEC xitn is 1o.  The broken symmetry is global
    gauge invariance.
  - ODLRO as corr len?!?  Ueltschi & Seiringer?!?
! pgr elx.txt et al. to Tom & Daniel.
! Type up Kevin Lin notes re FSS
! Type up DU notes
! What is DU's "slope" for phase-xitn plot
* SE = SD/sqrt(N); 95% CI = M += 2 SE.
* Error bars everywhere.
* Finer forkplots for N2.
* 3D Matlab color plot for f(L,T,alpha)
* Estimate Delta T_c as-is from hand-fit plots, with error bars
* 1st limlim:
  - loglog fit doesn't work.
  - fork analysis -- requires more experiments
  - handfit -- do-able with current data?  Write it up ...
  - Come up with L->infty plots ... extrapolate manually from the fork plots?
* 2nd limlim:
  - does loglog fit work here?
  - fork analysis?
  - handfit?
* rename tca files ...

Coding:
* Need to be able to ^C and/or ^\ out of taskutil stuff ...
* More RVs:
* Winding number
  ! Why is the superfluid fraction not a fraction?
  - Even with cycle reversals, ri=0 and ri=1 give different winding numbers
    at supercritical temperatures.  There's an occasional winding cycle or
    two which doesn't go away.  Topology ... look at dot plots.
  - Merge clat and cnell ...
  - !! cnell has a different rho shape!  current peak detection won't work.
! Code up alpha_ell on the lattice.
  - At MCMC level, array of alpha_ell.
  - Choice:  spec for 2; 2,3; 2,3,4; constant; alpha_2 sqrt n; ... ?
  - cutoff after specified length
  - N2 flag ...
* ICE
  - va, id, groups; qsub {script}, qstat, qdel -W force {ID}

Experiments:
* More experiments for N2:
  - alpha from 0 to 1 as at present -- including 0.02,0.05, 0.08.
  - L as at present
  - T from 6.80 to 7.20 much more finely
  - vary Ts on alphas -- ?

Misc:
* Look up quenched (lattice/fixed) and annealed (continuum avg): spin glasses
* Does rho_c^alpha for the lattice resemble the continuum result?
  N_2 and N_ell.  (Here it's T_c^alpha of course.)

* Read:
  - Feynman
  - HK

alpha T_c(alpha)(rough)
----  ----------
0.00  6.88
0.01  6.88
0.10  6.89
0.20  6.96
0.50  7.04
0.80  7.08
1.00  7.12

alpha   =   0.5000000
Tc0     =   6.8800000
Tcalpha =   7.0400000
Delta   =   0.0232558
a       =   0.0375893
c       =   0.6186825

alpha   =   0.8000000
Tc0     =   6.8800000
Tcalpha =   7.1200000
Delta   =   0.0348837
a       =   0.0598040
c       =   0.5833010

#Old:
##alpha T_c(alpha)? #idx
##----  ----------  #---
#0.00  6.88        #9
#0.01  6.88        #9
#0.10  6.92        #8.5
#0.20  6.96        #8
#0.50  7.04        #7
#0.80  7.12        #6
#1.00  7.12        #6
##
## alpha T_c(alpha)?
## ----- -----------
## 0.0   6.88
## 0.8   7.12
##
## 0.034 = c a
## alpha = 0.8
## alpha = sqrt(8.0 * pi / beta) * a
## a = sqrt(1.0 /8.0 * pi * T) * alpha
##   = sqrt(1.0/8/3.1416/7.12)*0.8
##   = 0.059804
## c = 0.034/0.0598
##   = 0.568562
##
# T
##6.88 9
##6.96 8
##7.04 7
##7.12 6
##7.20 5
##7.28 4
##7.36 3
##7.44 2
##7.52 1

----------------------------------------------------------------
Next-semester plans:

* HK correlation length:

  - (1) 2nd qtzn:  ODLRO:  <a^*(x) a(y)>.

  - (2) Gibbs operator exp{-beta H} in L^2_sym(Lambda^N).
    Integral kernel L(X,Y) w/ X=x_1..x_N and Y=y_1..y_N.
    See paper of Ueltschi & Seiringer?  Check against comp.pdf.
    (exp{-beta H})f(X) = int dY L(X,Y) f(Y).
    L depends on too many variables ...
    gamma(x,y) = 1/? int_{R^d(N-1)} L(x,x_2,..,x_N, y,y_2,...y_N)dx2..dxN.
    ?normalization:  int_{R^d} gamma(x,x)dx = 1 or N?
    Computable explicitly in the independent case.
    gamma decays exponentially (in T?) above T_c.
    exp{-||x-y||/gamma} -- ?
    Applies to Bose gas in the absence of BEC.
    Diverges near T_c.

* Understand where the Riemann-integral V_ij comes from.

* Importance sampling for pretabulated Riemann-integral V_ij.

* Somehow bootstrap for a=0 cyclen distributions to choice of alpha_ell's
  for the V_ij model?  Is it even *possible*, though ... winding numbers?

* Somehow do some estimations of averaged V_ij's to fit a curve for
  alpha_ell's in terms of a?
 
  - We will likely need another level of hierarchy:  interactions within
    and across cycles.
    sum_{ell=1}^N alpha_ell N_ell(pi) = sum_{c in pi} alpha_{ell(c)}.
    c's are cycles in cycdec.  Work this out separately.
  - DU guess:  TJI mean-field should be
    sum_{c in pi} alpha_{ell_c} + sum_{c,c'} beta_{ell(c),ell(c')}.
  - test it by retaining only N_1 & N_2.

* Understand the PIMC and psi^4 models.

----------------------------------------------------------------
Maybe:

* On S_N (no spatial structure):  lim_{n \to\infty} E(f_{1,sN}) = s.
  (look that up in BU08)
  - Easy for Urand.
  - True (BU) even for alpha_ell \ne 0 but downto 0:
    lim ... = 1-(1-s)^{e^-alpha}
  - For alpha up but not too fast:  some unpublished results.
  Ewens distribution -- ?
  Is this the 1x1 plot shape?

* What to expect for spatial permutations, on the lattice and/or continuum?

----------------------------------------------------------------
Non-plans:

* Choosing alpha_ell's corresponding to continuum V_ij (with average
  over positions):  too hard.  BU have something (first-order exact,
  unpublished) about interactions within cycles, but not across cycles.  Also
  it's not good for long cycles, esp. w/r/t higher winding numbers.

  Effective weights, mean-field ...