I can't think of anything that wouldn't be worse than ivy. How about creating a DMZ about a foot wide that you could use the string trimmer on once a week when you edged the lawn? Wouldn't stop it, but would be easier to control.

I've been pulling for a few years. Interestingly, the first round really did get most of it (90%, pretty shady area and the soil is quite loose from years of decomposing leaves which might help my cause some), and each year I have to pull up bits that are bounding back. By now, forth year, there is not much cropping up. Just so you know it isn't impossible.

I left a strip of it in a steep part of that garden, to prevent erosion until I could replace with something more interesting. That area I have to control heavily as it creeps into everywhere else. I may start replacing this season with either ajuga or creeping jenny or both. Haven't decided for sure.

Ha! You're right - other people's ivy is cool! (You mean hedera helix, english ivy, right? That's what I'm gonna talk about :+)

I think you might end up with 2 problem plants instead of 1 with the "thug war" method though... If I was going to try it, which I wouldn't, I guess I'd choose grape ivy. At least it's a native.

Is it possible to remove the ivy and install a physical barrier in this site?

Do you know that your neighbors are "into" the ivy, or is it maybe just there for so long nobody knows why? Maybe they'll follow your example if you get rid of yours and make that spot pretty with some well-mannered, attractive plants. Bad news: removing this ivy is hard shovel-work. Good news: Once you dig it out, it should be gone unless sprouts come up. Do you know if it makes seeds where you are?

Here is a link that might be useful: you can find your zone here