近期，Perk教授及夫人与本人通了多轮e-mails就三维伊辛模型的问题进行学术讨论。应Perk教授及夫人的要求（以及我征求他们的同意），本人将在博客中陆续公开他们的e-mails以及本人的答复意见。Perk教授也曾经在他中e-mail指出，科学网博客应该做为一个学术交流和讨论的平台，而不是一个社会公众争议的场所。这与本人的观点非常一致。所以，为了集中于学术讨论，本人将屏蔽掉e-mails中的非科学内容（用……表示）。为了正确完整地反应交流中的学术思想，将不对e-mails做任何翻译。 

       首先公开Perk教授上个月以及本月初的四封来信和我的回复：

       Perk教授2月24日将他写给王志明先生的一封e-mail转发给我。因为在这之前王志明先生已经在他的博客中公开了这封e-mail，信中没有说明来意。我不太明白Perk教授的意思，就写了一封e-mail询问，Perk教授又回复一封e-mail，说如果我愿意可以将两封信同时公开。 欢迎广大读者理性批评指教。

> My understanding that Zhang admits his results are wrong comes from the English in his email in reply to my wife's
 email and that he has posted in his blog. He said that he
> learned a great deal from my Comment / Rejoinder and also
> emails.  Not going into possible errors in intermediate steps,
> we should only look at his answers for the free energy
> and the magnetization, his two main results. They are
> both analytic in 1/T at T = temperature = infinite.
> The corresponding series expansions do not agree with
> those published by many experts and even derived in
> many graduate student classes. This is the point in
> the Comment of F.Y. Wu, McCoy, Fisher, and Chayes,
> four of the leading world experts on the Ising model.
> Zhang gives as the explanation that the results must
> have a phase transition of sorts, meaning that the
> free energy and magnetization are not analytic at
> T = infinite. This is by itself a serious internal
> contradiction in Zhang's work, which I pointed out
> in my Comment, concerning the magnetization.
> In my Rejoinder I prove that this assertion is also
> in direct violation of the famous 1952 papers of
> C.N. Yang and T.D. Lee, the Chinese Nobel Prize
> winners. This is the thing to be learned from my
> Rejoinder. Therefore, I concluded that Zhang admitted
> that the final answers in his paper are wrong.
> I am sad that his inner voice tells him that the
> conjecture is still OK. Science is a hard fight to
> find out the truth, on which we all agree. Heated
> discussions are normal, but we like to see nobody
> hurt as we come to the truth. Thus we attack each
> others thoughts, while we respect each person. I
> hope that reason will win and that Zhang will
> recognize his inner voice as a lying spirit, who
> is only out to hurt him. This is my prayer for him.
> Best regards,
> Jacques H.H. Perk
我的回复(2009-2-26)：

Dear Prof. Perk:

Thanks for sending this e-mail to me, which had been opened in Mr. Wang Zhiming's blog. So, I wonder what your meaning is. Do you mean that you wish to open it also in my blog. If so, please let me know.

Best wishes,

Zhidong Zhang

> Dear Dr. Zhang,
> >………………………………………………….

 Most of the email is a short summary of the comments
> and rejoinders. The statement about Yang and Lee
> is an other misunderstanding you have, shortly
> discussed in the rejoinder. Yang and Lee talk about
> zeros moving from z=-1 at T=infinity to z=+1 at
> T_c, the critical point. The simple calculation I
> gave in the rejoinder locates the critical point
> at T=infinity, H=i*infinity. You may not think that
> that is enough detail. But the rejoinder did not
> give space to go into further detail.
> There are many papers proving analyticity in 1/T
> around T=infinity, by many groups in Europe, Russia,
> Japan and America, for classical and quantum models
> that generalize the Ising model. I quoted a few
> mostly Ising references. The exactness of the series
> is rigorously proved many times. It is also backed
> up by numerical work as Pade analysis of the series
> agree excellently with Monte Carlo calculations.
> There is no such evidence backing up your work,
> as your work violates rigorous theorems.

………………………………………………….
> > You can post this and the other email if you want.
> Sincerely,
> Jacques H.H. Perk

PS: …………………………………………
>
我的回复(2009-2-27)：

> Dear Dr. Perk:

Thanks for your e-mails. As stated in my blog, I am very grateful for all of discussion with you via your Comment/Rejoinder and e-mails.

I respect your objections on my work, and your comments push me to study the problems in deeper.
I have already posted my additional response as the second part of 0812.0194v3. Any further comments from you are welcome. 
Sincerely,
Zhidong Zhang

Dear Dr. Zhang,

I cannot submit immediately, as I have deadlines to do other things. But your logic is wrong: The probability interpretation of statistical mechanics involves Z and thus beta f. Therefore, f by itself going to infinity as T goes to infinity is of no physical significance. Series and analyticity determinations must be starting from beta f = f/kT, not f. Also, as long as the real part of f is negative, (which is easily checked for the Ising model at arbitrary temperature), Z=exp(-N beta f) blows up and 1/Z goes to zero as N goes to infinity. So zeros of 1/Z as N goes to infinity occur also for all finite temperatures even at the critical point where the Yang-Lee zeros pinch the real axis. It is a misinterpretation of the Yang-Lee papers to study zeros of 1/Z.

Sincerely,

Jacques H.H. Perk

 

 

Dear Dr. Perk:

 

Thanks for your fast reply. Any further comments are welcome. 

I feel that at the moment, it is not very suitable for opening your previous two e-mails in my blog. However, if you did not mind, I would post the part focusing on scientific issues in future when the time is suitable. Thanks for your understanding.
Best wishes,

Zhidong Zhang

Dear Dr. Zhang,

I have updated arXive:0901.2935 with more details than in my email to you. I hope it is useful to you. I will not be able to reply in the near future, as I must address urgent other matters. …….

Sincerely, Jacques H.H. Perk

Dear Dr. Perk:

Thanks for your added comments. I shall let you know if I response to it.
Best wishes, to Helen and you!

Zhidong Zhang